Social Network Analysis in Education

Contents

List of Tables vii

List of Figures ix

Preface xi

Syllabus xv

Introduction xvii0.1 What is Social Network Analysis? . . . . . . . . . . . . . xvii

0.2 Why Social Network Analysis? . . . . . . . . . . . . . . xvii

0.2.1 Student perspectives . . . . . . . . . . . . . . . xvii

0.2.2 The hidden influence of social networks . . . . . xviii

0.3 Syllabus . . . . . . . . . . . . . . . . . . . . . . . . . . xviii

0.4 Digital learning environments . . . . . . . . . . . . . . xviii

0.4.1 Bookdown course site . . . . . . . . . . . . . . . xix

0.4.2 Slack (UMN Students Only) . . . . . . . . . . . . xix

0.4.3 Hypothesis . . . . . . . . . . . . . . . . . . . . xx

0.4.4 Twitter (optional) . . . . . . . . . . . . . . . . . xxi

0.4.5 Google Drive . . . . . . . . . . . . . . . . . . . xxi

0.4.6 Integrations . . . . . . . . . . . . . . . . . . . xxii

0.5 Week 1 Activities . . . . . . . . . . . . . . . . . . . . . xxii

0.5.1 Get to know each other . . . . . . . . . . . . . . xxiii

0.5.2 F2F sessions . . . . . . . . . . . . . . . . . . . xxiii

0.5.3 Readings & Annotations . . . . . . . . . . . . . xxiii

Basic Concepts xxvii0.6 Understanding SNA in Educational Research . . . . . . . xxvii

0.6.1 Three levels of considerations . . . . . . . . . . xxvii

0.7 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . xxix

0.8 Week 2 Activities . . . . . . . . . . . . . . . . . . . . . xxxi

iii

iv Contents

0.8.1 Read & Annotate . . . . . . . . . . . . . . . . . xxxi

0.8.2 Draft an intial project idea . . . . . . . . . . . . xxxii

Applications and Examples I xxxiii0.9 Applications and Examples of SNA . . . . . . . . . . . . xxxiv

0.10 Week 3 Activities . . . . . . . . . . . . . . . . . . . . . xxxiv

0.10.1 Readings . . . . . . . . . . . . . . . . . . . . . xxxv

0.10.2 Share & Take . . . . . . . . . . . . . . . . . . . xxxvi

Collect and Manage Network Data xxxix0.11 Understanding SNA Data . . . . . . . . . . . . . . . . . xl

0.11.1 Sources of SNA data . . . . . . . . . . . . . . . xl

0.11.2 Totality and sampling . . . . . . . . . . . . . . . xli

0.12 Ethics in SNA research . . . . . . . . . . . . . . . . . . xliii

0.13 Linear algebra basics . . . . . . . . . . . . . . . . . . . xliii

0.14 Managing SNA data . . . . . . . . . . . . . . . . . . . . xliv

0.14.1 Basic representations . . . . . . . . . . . . . . . xliv

0.14.2 Two-mode data . . . . . . . . . . . . . . . . . . xlvi

0.15 Import data into software . . . . . . . . . . . . . . . . . xlviii

0.15.1 Track R . . . . . . . . . . . . . . . . . . . . . . xlix

0.15.2 Track Gephi . . . . . . . . . . . . . . . . . . . . l

Sociograms and Density li0.16 Sociograms and network visualizations . . . . . . . . . lii

0.16.1 Example 1: Global Flight Network . . . . . . . . . liii

0.16.2 Example 2: Networks of interaction in mobile ani-mal groups . . . . . . . . . . . . . . . . . . . . liv

0.16.3 Example 3: Migration Network . . . . . . . . . . liv

0.16.4 Example 4: Light Up the Curriculum . . . . . . . lv

0.16.5 Play more with network visualizations . . . . . . lvi

0.17 Density and Other Structural Measures for Complete Net-works . . . . . . . . . . . . . . . . . . . . . . . . . . . lvi

0.18 Assignments and Activities . . . . . . . . . . . . . . . . lix

0.18.1 Read and build knowledge . . . . . . . . . . . . lix

0.18.2 Assignment: Data collection hands-on . . . . . . lx

0.18.3 Compute network-level measures and share . . . lxi

Centrality and Centralization lxiii

Contents v

0.19 Centrality and Centralization: An Overview . . . . . . . lxv

0.20 Betweenness Centrality . . . . . . . . . . . . . . . . . . lxvi

0.21 Eigenvector Centrality . . . . . . . . . . . . . . . . . . lxvi

0.22 Week 6 Activities . . . . . . . . . . . . . . . . . . . . . lxvi

0.22.1 Readings . . . . . . . . . . . . . . . . . . . . . lxvi

0.22.2 Compute Node-level Measures . . . . . . . . . . lxvii

Components and Cliques lxix0.23 Introduction to Components and Cliques . . . . . . . . lxix

0.24 From Data to Analyses: A Demo . . . . . . . . . . . . . . lxix

0.25 Assignments and Activities . . . . . . . . . . . . . . . . lxx

0.25.1 Read, Annotate, and Share . . . . . . . . . . . . lxx

0.25.2 Project Checkpoint 2 . . . . . . . . . . . . . . . lxx

Ego-centric Networks lxxiii0.26 Introduction to Ego-Centric Networks . . . . . . . . . . lxxiv

0.27 Collecting Ego-Centric Data . . . . . . . . . . . . . . . lxxvi

0.27.1 “Les Miserables” Example . . . . . . . . . . . . . lxxvi

0.28 Analyzing Ego-Centric Networks . . . . . . . . . . . . . lxxviii

0.28.1 Track R . . . . . . . . . . . . . . . . . . . . . . lxxix

0.28.2 Track Gephi . . . . . . . . . . . . . . . . . . . . lxxix

0.29 Week 8 Activities . . . . . . . . . . . . . . . . . . . . . lxxx

Applications and Examples II lxxxi0.30 Week 9 Activities . . . . . . . . . . . . . . . . . . . . . lxxxi

0.30.1 Read, Examine & Share . . . . . . . . . . . . . . lxxxi

0.30.2 Comment . . . . . . . . . . . . . . . . . . . . . lxxxii

0.30.3 Lists of articles to choose from . . . . . . . . . . lxxxii

0.31 Course Project Check-in . . . . . . . . . . . . . . . . . lxxxiv

0.31.1 Use an R Notebook . . . . . . . . . . . . . . . . lxxxv

Statistical Analysis with Network Data lxxxvii0.32 Introduction . . . . . . . . . . . . . . . . . . . . . . . lxxxvii

0.33 Week 10 Activities . . . . . . . . . . . . . . . . . . . . . lxxxviii

0.33.1 Additional resources . . . . . . . . . . . . . . . lxxxix

0.34 Course Project Check-in . . . . . . . . . . . . . . . . . lxxxix

Network Dynamics and Temporality xciii

vi Contents

0.35 Class Google Hangout . . . . . . . . . . . . . . . . . . xciii

0.35.1 Tools for temporal network analysis . . . . . . . xciv

0.36 Week 11 Activities and Upcoming Milestones . . . . . . . xciv

0.36.1 Week 11 activities . . . . . . . . . . . . . . . . . xciv

0.36.2 Upcoming milestones . . . . . . . . . . . . . . xcv

Planning SNA Research and Projects xcvii0.36.3 Week 12 activities . . . . . . . . . . . . . . . . . xcvii

0.36.4 Upcoming milestones . . . . . . . . . . . . . . xcviii

Novel Approaches and Analytics xcix0.37 Resources and Activities . . . . . . . . . . . . . . . . . xcix

0.37.1 Resources . . . . . . . . . . . . . . . . . . . . . c

0.37.2 Reflect and Share . . . . . . . . . . . . . . . . . ci

List of Tables

0.1 Table 1. A table of nodes. . . . . . . . . . . . . . . . . . . xlv0.2 Table 2. A table of weighted ties . . . . . . . . . . . . . . xlv0.3 Table 3. A table of raw data of ties. . . . . . . . . . . . . . xlvi0.4 Table 4. Sports teams in the school. . . . . . . . . . . . . xlvi0.5 Table 5. Student affiliation with sports teams. . . . . . . . xlvii0.6 Table 6. Sports teams in the school (version 2). . . . . . . . xlvii

0.7 Table 5.1: Different types of networks. . . . . . . . . . . . lvii

vii

List of Figures

1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . liii

2 Gephi Graph Overview. . . . . . . . . . . . . . . . . . . lxviii3 Gephi Data Laboratory. . . . . . . . . . . . . . . . . . . lxviii

ix

Preface

This site is the course portal of CI5330 - Social Network Analysis in Educa-tion, taught by Prof. Bodong Chen1 at the University of Minnesota in Spring’17.

Content on this site is actively built and refined throughout the semester.

Key links for the course

• Textbook Carolan (2014)2. Note: UMN library access required.• Slack team3: We use Slack for course “management”, aka. announce-

ments, commucations, chats, small group work, etc.• Hypothesis4: We interact on top of web materials (including the text-

book) during this course. Hypothesis is a cutting-edge, open-source webannotation tool, which is used more and more broadly by educators5 inthe past two years.

• Optional - Twitter hashtag #SNAEd6: You can tweet about this courseusing #SNAEd.

This site or book is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License7.

Last update: 2017-04-17

1http://bodong.ch2http://methods.sagepub.com.ezp1.lib.umn.edu/book/

social-network-analysis-and-education3https://snaed.slack.com/4https://hypothes.is/5https://hypothes.is/education/6https://twitter.com/search?q=%23snaed7http://creativecommons.org/licenses/by-nc-sa/4.0/

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xii Preface

Why not Moodle for this course?

To learn social network analysis (SNA) – and many other stuff – I believe thebest way is to ‘live’ with it. That is, the best way to learn SNA is to seize everyopportunity of applying SNA in one’s own learning journey. This philosophyleads to two major reasons I’m piecing together a learning environment bymyself:

• First, as an instructor I wish to foster social interactions as much as pos-sible. Traditional learning management systems like Moodle is limitingfor this purpose.

• Second, to practice SNA with our own ‘learning traces’, system log data8

need to be somehow exposed to users. Traditional systems are fallingbehind in this area.

If you haven’t used these tools mentioned above, no worries. I will providedetailed guidelines to get you started (see Section 0.4). Many of us would beventuring out of our comfort zones. (SO DO I – because this is the first time Iam doing this :-).) I hope we will all learn a great deal about SNA and beyond.

Have fun!

Two tracks of participation

This course website is openly available online, reflecting my committmentto ‘open scholarship9’. So there are two tracks of participation designed forthis class.

1. UMN class: For UMN graduate students enrolled in the class, your

8Note that the description of models introduced here may not fit the philosophicalworldview you feel comfortable with or subscribe to. Refer back to Section @ref{three-levels} for an earlier discussion we had about aligning methodology and philosophical view-points.

9http://bodong.ch/notes/

Preface xiii

participation in this class is not that different from taking anotherprimarily online class. You are expected to meet course require-ments outlined in the course syllabus. You will have a private space(supported by Slack) for within-class communications.

2. Open participation: For ‘Open Participants’ who are following theclass, you can access the same materials I curate on this website.You may need to buy the textbook if you do not have a library ac-cess. And ways for you to participate include 1) making Hypothesisannotations using #SNAEd (more later), and 2) discussing in anopen forum10.

If you have any feedback on the current design, please get in touch. I’d loveto hear your thoughts.

Ways to contribute to this site

This is the first time I am offering this course and teaching in such an ‘open’manner. By making this course site open, I hope it could be useful beyondour current class. So I’d appreciate your help to continually improve the site.

1. The best way to contribute to this site is to annotate it using Hy-pothesis11. For example, to point out a possible spelling error, youcan highlight the error and include two tags – SNAEd and issues –in your annotation.

2. The second best way is to report a New Issue on this website’sGithub issues page12.

3. If you’re Github-savvy, please consider forking the Github reposi-tory13, making edits, and sending me a pull request.

4. If none of those options work for you, simply drop me an email atchenbd@umn.edu.

10https://muut.com/snaed/11https://hypothes.is/12https://github.com/meefen/sna-ed/issues13https://github.com/meefen/sna-ed/

Syllabus

The most up-to-date syllabus is here14.

14https://github.com/meefen/sna-ed/blob/master/syllabus/syllabus.md

xv

0

Introduction

This week we will:

1. Get to know each other2. Walk through the Syllabus3. Get to know course logistics

Please click on the ‘>’ button to proceed to the next page.

0.1 What is Social Network Analysis?

Please watch the following short video made by colleagues from Duke.

Credit: ModU: Powerful Concepts in Social Science15

0.2 Why Social Network Analysis?

0.2.1 Student perspectives

We come together to learn (more) about social network analysis (SNA) –for various reasons. In preparation for the class, I invited three currentgraduate students – Alejandro Andrade from Indiana, Michael Brown fromUMich, and Fan Ouyang from UMN – who’re all doing interesting work with

15https://www.youtube.com/channel/UCDfHkEuoKb_TXYkQY6BkIIg

xvii

xviii Introduction

SNA to share a bit about their experiences (note some videos are only visiblefor UMN viewers):

Alejandro Andrade

Michael Brown

Fan Ouyang

Getting inspired? You will have a chance to share your interests in SNA inSection 0.5.

0.2.2 The hidden influence of social networks

0.3 Syllabus

The most current syllabus16 will always available online.

In Week 1, please read the Syllabus in full. Ask questions, if any, on the#q_and_a channel on Slack.

0.4 Digital learning environments

This is a primarily online class. We will use a range of digital tools to supportour individual and group learning. As I explained in Preface17, I hope to sup-port ‘learning-by-doing’ experiences in this SNA class. One way to achievethis is to foster social interactions among us and analyze traces of our owninteractions. This design idea has played an important role in the choices ofdigital environments.

Below is a list of them and we could tweak the list when moving forward.

16https://github.com/meefen/sna-ed/blob/master/syllabus/syllabus.md17https://bookdown.org/chen/snaEd/why-not-moodle-for-this-course.html

Digital learning environments xix

0.4.1 Bookdown course site

This website you’re reading is built by myself using Bookdown. Bookdown isdesigned for writing books. While this site may evolve into an open textbook,I’m using it as our course portal.

Course resourses, usually organized by weeks, will be published here. Eachchapter maps onto a week. Weekly course annoucements will be pushed tothe class through Slack (more below). (If you are an ‘Open Participant’, justcheck this website once in a while. I will update the site on Mondays.)

0.4.2 Slack (UMN Students Only)

Slack is a team communication tool popular among tech companies and in-creasingly adopted in classrooms. It was originally created to make team-work more efficient – and more fun. The reason we’re using Slack, insteadof emails or an LMS, is its support for dynamic communication among allparticipants.

In SNAEd, we will rely on Slack – instead of an LMS – for class communi-cation. For instance, I will use Slack to push out course annoucements, dis-tribute materials, collect assignments, organize small groups, provide feed-back, etc. You can use Slack to discuss with each other, self-organize intogroups, contact me for feedback, share funny gifs, etc. In a sense, we workas a team where everyone can – and is expected to – initiate things. In thisonline class, all participants, including me, are expected to check Slack sev-eral times a week.

To sign up for our private Slack team, go to: https://snaed.slack.com/signup

To get started with Slack, get familiar with a few Slack terms you need toknow 18:

18Note that the description of models introduced here may not fit the philosophicalworldview you feel comfortable with or subscribe to. Refer back to Section @ref{three-levels} for an earlier discussion we had about aligning methodology and philosophical view-points.

xx Introduction

• Messages or Updates — the basic message or status of Slack. Similar toFacebook updates, tweets, chats, etc.

• Channels — like separate rooms within the domain. They can be public orprivate.

• Direct Messages — like DMs or private messages anywhere else.• Posts — longer than a status update. Similar to a blog post or a Word doc-

ument. Once it’s shared to a Channel, folks can comment on it or even editit if the owner allows.

• Snippets — Chunks of syntax-highlighted code for when that’s the thingyou need to share. We might use it.

• @replies — much like on Twitter, used when you want to mention some-one. You can @everyone or @channel.

• emoji — just like what you see everywhere.• Integrations — Slack can ‘talk’ with many other systems. For example, you

can post a doc from your Google Drive when submitting an assignment;you can type /giphy to share random gifs. I will explain more later.

Knowing those should be enough for the class. To learn more, checkout the Slack tutorials: https://get.slack.help/hc/en-us/categories/200111606-Using-Slack

0.4.3 Hypothesis

Each week when we read, we will be making social annotations in Webdocuments using a cutting-edge tool named Hypothesis (Hypo for shorthereafter). This is to replace threaded discussion in typical online classes. Thereason we’re interacting through social annotations instead of posting inthreaded discussions is Hypo supports 1) more situated discussions aroundcourse materials; 2) dynamic interactions in a broader web space; and 3) flex-ible retrieval of our annotations (ideas) through Hypo’s search functionality.As such, I wish social annotations we make each week could remain ‘alive’(not stuck in threads) and useful for later phases of our individual or groupwork.

Hypo has been used broadly in education, for example, for close reading inhumanities (Kennedy, 2016). In this class, the basic idea is we are going toengage with Web materials (e.g., our textbook accessible from the libary)

Digital learning environments xxi

and interact with each other through reading & commenting on each other’sannotations.

To set up Hypo for the class:

• Register an account here: https://hypothes.is/register, and join ourgroup at https://hypothes.is/groups/8Nxk21z5/snaed

• Install the Hypo extension19 in your Google Chrome browser.

Using Hypo - important tips:

• Include theSNAEd tag in every annotation you make for the class. Otherwise,it will not be picked up by our class feed20.

• Monitor our class feed here: https://hypothes.is/search?q=tag%3ASNAEd• Reply to each other’s annotations

To learn more, check out Hypothesis Quick Start Guide for Students21, anda more complete Resource Guide for Students22.

Note: Please try to use a same (or at least a smilar) username for Slack andHypo so that we can match you in two spaces.

0.4.4 Twitter (optional)

If you tweet, like me23, please tag your tweets with #SNAEd as well.

To demonstrate how Twitter could be useful, I bet you can learn more fromTechPizza24 than from this course (set Topic to be, for example, ‘Text, Net-work Analysis’ –> ‘network:gephi’).

0.4.5 Google Drive

Google Drive will be used for major assignment submissions. I will pro-vide detailed feedback directly in your Google Docs, so it is important you

19https://chrome.google.com/webstore/detail/hypothesis-web-pdf-annota/bjfhmglciegochdpefhhlphglcehbmek?hl=en

20https://hypothes.is/search?q=tag%3ASNAEd21https://hypothes.is/quick-start-guide-for-students/22https://hypothes.is/student-resource-guide/23https://twitter.com/bod0ng24http://techpizza.org/twitter.php

xxii Introduction

use Google Drive. UMN offers free Drive access and unlimited storage.If you need help, check this OIT page: https://it.umn.edu/technology/google-drive

To submit an assignment through Slack, head to the #assignment Slackchannel and click on the ‘+’ button to pull out a menu with opitons of addingDrive files. You may need to authenticate Google Drive on Slack. See helppage25.

0.4.6 Integrations

We are using multiple systems in this class. And I am fully aware that it maycause disorientation especially in the first one or two weeks. Please keep inmind Slack is the place for us to hang out, and other things – course contenton our course site, Hypo, Drive – will be somehow integrated in our commu-cations on Slack.

• Course site -> Slack: When new content is published (weekly in most cases),I will send out an annoucement in the #annoucement channel.

• Hypo -> Slack: Hypo annotations properly posted using our #SNAEd tag willbe notifed in Slack’s #hypo_feed channel.

• Drive -> Slack: You can directly add Drive files into Slack when submittinga ‘larger’ assignment (e.g., project paper, presentations, essays).

• Slack -> Email: Depending on your preference settings, you will receivesome notification emails from Slack. The default settings will email youPrivate Messages. You can change your email preferences here26.

0.5 Week 1 Activities

Below are a list of activities for Week 1. They are all due by Jan 23, 23:59PM,but I strongly encourage you to get started as early as possible!

25https://get.slack.help/hc/en-us/articles/205875058-Google-Drive-for-Slack26https://snaed.slack.com/account/notifications

Week 1 Activities xxiii

0.5.1 Get to know each other

Please record a short Flipgrid video to introduce yourself to the class. Thisactivity is important for this primarily online class. You should be able torecord following this link: https://flipgrid.com/3b6043

After recording your self-intro video, please check each other’s videos andrespond. Don’t feel shy about pointing out your shared interests or one class-mate’s nice wall decorations :-). (Tip: Test your sound to make sure it works.)

0.5.2 F2F sessions

To determine when will be a best weekday for us to meet F2F (or syn-chronously online), please respond to this Doodle poll27. It is important forus to list all possible time slots so we can find a time that work for all of us.

By the way, office hours will be provided each week. You can make appoint-ments with me here28.

0.5.3 Readings & Annotations

Read and annotate the following texts

• Carolan, ch. 129

• Borgatti, S. P., Mehra, A., Brass, D. J., & Labianca, G. (2009). Network anal-ysis in the social sciences30. Science, 323(5916), 892–895. (Note: enter here31

if you’re a non-UMN participant.)

When annotating, please try to do at least one entry for each of the following:

• Annotate an SNA term you find interesting/useful, and provide a defini-tion. Use tags term and SNAEd in your annotation

27http://doodle.com/poll/gyc992bdse6t28kq28https://calendar.google.com/calendar/selfsched?sstoken=

UUdPWnJUMWdoVnFJfGRlZmF1bHR8ZTNhZmQwOTNkYTE3ZjE2ZDVhMzI4MWY3MmJjZjExMjY29http://methods.sagepub.com.ezp1.lib.umn.edu/book/

social-network-analysis-and-education/n1.xml30http://science.sciencemag.org.ezp2.lib.umn.edu/content/323/5916/892.full31http://science.sciencemag.org/content/323/5916/892.full

xxiv Introduction

• Annotate an example application of SNA in readings, and explain how youfind it useful or interesting. Use tags application and SNAEd in your anno-tation

• Reply to annotations made by other participants

Below is an aggregation of our Hypo annotations so far.

Week 1 Activities xxv

32

32https://hypothes.is/search?q=tag%3Asnaed

xxvi Introduction

Have a wonderful week!

0

Basic Concepts

You’ve done an absolutely wonderful job on Flipgrid and Hypothesis! So ex-cited to see you joining this course from near (LES Building) and far (yesPauline, I am talking about you!). From our Flipgrid videos, I was amazedby the range of perspectives you’re bringing into this class! As many of youmentioned in your videos, we’re going to learn a lot from each other.

In this week, we will:

1. Explore social network perspectives2. Become familiar with basic SNA concepts3. Draft an initial SNA project idea and share out

0.6 Understanding SNA in Educational Research

0.6.1 Three levels of considerations

In the previous video, I described three levels of considerations that edu-cational researchers often need to be aware of. You could find more infor-mation in text such as (Niglas, 2010) or some other research methodologycourses. Please note that this framework was constructed to help us grapplewith the complex terrain of research, and it is highly debatable.

Below, I try to re-iterate the key message of the video – but from the bottomup:

• m, or methods/techniques: The “small m” in SNA constitutes methods ortechniques we apply in SNA research. Imagine we are using SNA to inves-tigate friendship of a network of high-schoolers (think about “Gossip Girls”

xxvii

xxviii Basic Concepts

if you’ve watched that TV series). A technique in this SNA research could bea questionnaire used to collect friendship data among students; it could bethe force-directed layout33 we use to visualize this network; it could be themeasure of betweenness centrality we use to characterize high-schoolers; itcould also be a network modeling algorithm we apply to model the flow ofgossips. In a nutshell, these techniques are more about what we concretelydo in an SNA research.

• M: When SNA is referred to as a “big M” Methodology, it is treated as a sys-tematic approach of investigating a phenomenon. Beyond simply applyingthese techniques, a methodology is also concerned with why a techniquegets used. In other words, understanding SNA as a methodology meanslearning to make informed decisions in any stage of an SNA project. For ex-ample, why using a questionnaire instead of observations or interviews? Inwhich cases should one use a circle layout instead of a force-directed layout?Why a specific SNA measure is appropriate for addressing a research ques-tion? In a nutshell, the big M is concerned with how knowledge could bebest gained by following many SNA methodologists and researchers havecreated so far.

• P, worldviews, philosophical schools of thoughts, paradigms: In SNA,some scholars go further to argue SNA offers a unique way of “seeing theworld.” In Carolan (2014) chapter 2 you will read about the relational per-spective that represent a particular worldview that emphasizes relationsinstead of attributes. You will also read about relational realism that is re-ferred to as an ontology grounding SNA. To a great extent, SNA offers anew research paradigm. As put by Barry Wellman, a guru in SNA from theUniversity of Toronto, “It is a comprehensive paradigmatic way of takingsocial structure seriously by studying directly how patterns of ties allocateresources in a social system” (see, Carolan, 2014, p. 33).

In this course, we are mostly concerned with the “big M” level. We will notdive too deep into the P level, and we will not settle with specific techniques.Together, we will learn how to apply various techniques to systematicallyproduce knowledge about a phenomenon.

33https://en.wikipedia.org/wiki/Force-directed_graph_drawing

Basic Concepts xxix

0.7 Basic Concepts

Last week, you’ve identified a wide range of terms from course readings. Seethe Hypo search results below:

xxx Basic Concepts

34

This week, we will be immersed in a number of key SNA concepts. In the fol-lowing video, I “glide over” some basic terms that are often used in SNA. You

34https://hypothes.is/search?q=tag:snaed%20tag:term

Week 2 Activities xxxi

do not need to memorize them all. As a matter of fact, I see those terms ex-isting as a network (see the image below); as you “unlock” one term, you arealso activating others. So spend time on some terms, and you’re implicitlylearning about others.

(Credit: Small World of Words project35)

0.8 Week 2 Activities

Due by Jan 30, 11:59PM

0.8.1 Read & Annotate

Read:35https://smallworldofwords.org/en/project/visualize

xxxii Basic Concepts

• Carolan, ch. 236, starting from “The Integration of Theory and Method”(pp. 32–42)

• Carolan, ch. 337

Annotate using Hypo. Like Week 1, please try to do at least one entry for eachof the following:

• Annotate an SNA term you find interesting/useful, and provide a defini-tion. Use tags term and SNAEd in your annotation

• Annotate an example application of SNA in readings, and explain how youfind it useful or interesting. Use tags application and SNAEd in your anno-tation

• Reply to annotations made by others

0.8.2 Draft an intial project idea

1. In Slack, in the assignments channel, share a post describing yourinitial project idea.

• In your post, use 3 paragraphs to (1) describe the context, (2) articulate thephenomenon and introduce your key question(s), and (3) describe any ini-tial thoughts (if any) on using SNA in this project.

• Not sure how to compose a post? Check this help page38.

2. Read each other’s posts. Please leave comments (and emojis if youwant) to “praise” and/or “push” each other.

(If you find someone who share a similar interest with you, you’re encour-aged to form a group. Slack is always there for you to communicate and col-laborate with each other!)

Have a wonderful week!

36http://methods.sagepub.com.ezp1.lib.umn.edu/book/social-network-analysis-and-education/n2.xml

37http://methods.sagepub.com.ezp1.lib.umn.edu/book/social-network-analysis-and-education/n3.xml

38https://get.slack.help/hc/en-us/articles/203950418-Compose-a-post

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Applications and Examples I

In Week 2, we explore basic concepts/terms in SNA and drafted our initialproject ideas. Below I am randomly highlighting two terms you explicated,and I encourage you to check out our Hypo Feed39 regularly.

sociometry

This has come up a couple times now with no definition (that I’ve seen), soI looked it up on dictionary.com: the measurement of attitudes of social ac-ceptance or rejection through expressed preferences among members of asocial grouping

– contributed by Val40

social capital

this is a fuzzy term, which was only reinforced as being fuzzy for me whentrying to find a more formal definition. I think this page41 summed it up thebest

– contributed by Lisa42

39https://hypothes.is/stream?q=tag:snaed40https://hyp.is/VvJoFOS9EeaJrhvFrHVA3Q/methods.sagepub.com.ezp1.lib.umn.edu/

book/social-network-analysis-and-education/n3.xml41http://www.socialcapitalresearch.com/literature/definition.html42https://hyp.is/Z-WUYucUEea1q7eJmEYkfA/methods.sagepub.com.ezp1.lib.umn.edu/

book/social-network-analysis-and-education/n2.xml

xxxiii

xxxiv Applications and Examples I

In this week, we will:

• Examine some concrete examples of SNA research• ‘Present’ an example of your choice to the class• ‘Take’ ideas from each other to inform your project ideas

0.9 Applications and Examples of SNA

After the first two weeks of exploration, I am quite sure we’ve come to a sharerecognition on the potential of SNA in various domains. In this page, I wantto share two applications of SNA – outside of education – that I found inspir-ing.

The first example is Suzanne Simard’s TED talk on “How trees talk to eachother” that I stumbled upon when listening to NPR. (Canadian accent alert!)The reason I picked this exmaple is Simard’s work demonstrates a paradigmshift (discussed by Barry Wellman in last week’s readings) in the study oftrees and forests by highlighting the importance of ties among trees.

The second example is Amar Dhand’s work on “stroke patients’ health be-haviors” that is based on a specific type of social network named ego-networks.The reason I picked this example is Dhand did a great job presenting the mo-tivation of their work and went on to investigate a solution powered by SNA.This presentation could be a great model for you to follow for this week’sclass activity (see next page for details).

Did you find these examples inspiring? Feel free to share on the Slack ideaschannel, or make Hypo annotations on this page using hashtags SNAEd &ideas.

0.10 Week 3 Activities

• Read & Share, due by Friday Feb 3, 11:59PM

Week 3 Activities xxxv

• Take / comment, due by Monday Feb 6, 11:59PM

0.10.1 Readings

1) Skim Carolan, ch. 10, on “Social Capital”43, and annotate conceptsyou recognize / don’t know

2) Closely examine an empirical study of your choice. You could ei-ther (a) claim one article from below – by annotating it using Hypo,or (b) search for one article from your research area. I would rec-ommend option #b so that this reading activity is adding to yourproject.

When examining the article, please try to discern those three levels of con-siderations I presented in Week 2 (i.e., Philosophical, Methodological, andmethods).

• Daly, A. J., & Finnigan, K. S. (2011). The Ebb and Flow of Social NetworkTies Between District Leaders Under High-Stakes Accountability. Ameri-can Educational Research Journal, 48(1), 39–79.

• Baker-Doyle, K. (2010). Beyond the Labor Market Paradigm: A Social Net-work Perspective on Teacher Recruitment and Retention. Education PolicyAnalysis Archives, 18, 26.

• Heck, R. h., Price, C. l., & Thomas, S. l. (2004). Tracks as Emergent Struc-tures: A Network Analysis of Student Differentiation in a High School.American Journal of Education , 110(4), 321–353.

• González Canché, M. S., & Rios-Aguilar, C. (2015). Critical Social NetworkAnalysis in Community Colleges: Peer Effects and Credit Attainment. NewDirections for Institutional Research, 2014(163), 75–91. https://doi.org/10.1002/ir.20087

• Hill, M. (2002). Network Assessments and Diagrams: A Flexible Friend forSocial Work Practice and Education. Journal of Social Work , 2(2), 233–254.

• Christley, R. M. (2005). Infection in Social Networks: Using Network Anal-ysis to Identify High-Risk Individuals. American Journal of Epidemiology,162(10), 1024–1031. http://doi.org/10.1093/aje/kwi308

43http://methods.sagepub.com.ezp1.lib.umn.edu/book/social-network-analysis-and-education/n10.xml

xxxvi Applications and Examples I

• Christakis, N. A., & Fowler, J. H. (2007). The spread of obesity in a largesocial network over 32 years. The New England Journal of Medicine, 357(4),370–379.

• Dawson, S., Tan, J. P. L., & McWilliam, E. (2011). Measuring creative poten-tial: Using social network analysis to monitor a learners’ creative capacity.Australasian Journal of Educational Technology, 27(6), 924–942.

• Honeycutt, T. (2009). Making Connections: Using Social Network Analysisfor Program Evaluation. Mathematica Policy Research, (1), 1–4.

• Rienties, B., Héliot, Y., & Jindal-Snape, D. (2013). Understanding sociallearning relations of international students in a large classroom using so-cial network analysis. Higher Education, 66(4), 489–504. http://doi.org/10.1007/s10734-013-9617-9

• Martinez, A., Dimitriadis, Y., Rubia, B., Gómez, E., & de la Fuente, P. (2003).Combining qualitative evaluation and social network analysis for the studyof classroom social interactions. Computers & Education, 41(4), 353–368.

• Roberson, Q. M., & Colquitt, J. A. (2005). Shared and Configural Justice: ASocial Network Model of Justice in Teams. Academy of Management Re-view. Academy of Management, 30(3), 595–607.

0.10.2 Share & Take

1) Share the article you read in a concise manner to the class. Thevideo on “stroke patients” in the previous page could be a greatexample to follow. In your sharing, you should cover:

• research problem and questions• collection of SNA data• specific use of SNA (e.g., specific SNA measures, visualizations)• key findings• one “praise” and/or one “push”

You can choose between these two formats:

• a screencast (5-min max): A video presentation of you talking through yourexample. Post a link to your video to the Slack assignments channel. Po-tential video capturing tools include Jing, QuickTime, and Screencast-O-Matic.

Week 3 Activities xxxvii

• a Slack post (500-word max): Post a text-based post to the Slack assignmentschannel as we did in Week 2.

2) Take ideas from each other’s presentations to inform your project.Comment on each other’s posts to acknowledge ideas you takefrom them, seek clarifications, etc.

Have a wonderful week!

0

Collect and Manage Network Data

In this week, we will:

• Get to know some key decisions SNA researchers need to make on datacollection

• Understand several data collection techniques• Understand processes involved in storage and transformation of SNA data• Practice importing data into SNA software• Become aware of ethical issues involved in SNA research

An overview of Week 4 activities:

• Read– Carolan, ch. 4– Book chapter on Ethical Considerations With Social Network Analy-

sis44

• Play & Share (more details on Section 0.15)– Import a practice dataset into the SNA software of your choice– Get familiar with the software– Share the network visualization you make in the assignment channel,

due by Monday Feb 13, 11:59PM

I’ve created two new Slack channels R and Gephi for track-specific questionsand discussions.

44https://open.lib.umn.edu/principlesmanagement/chapter/9-5-ethical-considerations-with-social-network-analysis/

xxxix

xl Collect and Manage Network Data

0.11 Understanding SNA Data

Blankly speaking, data collection in SNA research is concerned with twotypes of data: (1) relational data that describe ties, and (2) attribute data thatdescribe nodes. For example, if I want to study friendship in a high schoolclass, depending on my research questions I may choose to collect attributedata of each student (such as gender, race, GPA), and relational data of everypossible pair of students (such as whether Student A texts Student B, or howmany times A texts B). Quite simple, right?

However, real-world SNA projects in education demand a number of criticaldecisions to be made by the researcher. Just to list a few examples:

• how to gain access to the research “field” (e.g., a student fraternity, an in-timate parent group)

• from whom are data collected (and who are excluded from data collection)• which instruments are used for data collection• how are data structured and stored• how to transform data to different shapes to address specific research

questions

In this week’s reading – Carolan (2014), Ch 4 – you will read detailed sugges-tions from the author. Below I briefly comment on a few key points, beforeengaging you in detailed techniques in later sections.

0.11.1 Sources of SNA data

SNA data may be obtained in a variety of ways—from historical archives,questionnaires, ethnographic studies, system logs of online platforms, etc.For example, from public records researchers could analyze co-sponsorshipof legislation in the U.S. Senate; from a classic Chinese novel, Dream of theRed Chamber45, researchers could use SNA to estimate relationships betweencharacters based on their co-occurrence (Zhao and Weko, 2016). In thesetwo cases, we can see that in SNA research some relational data are naturalor readily available (e.g., co-sponsoring of a legislature), while some other

45https://en.wikipedia.org/wiki/Dream_of_the_Red_Chamber

Understanding SNA Data xli

need to be derived (e.g., relationship between novel characters based on co-occurrence of names in a same sentence).

No matter how relational data get gathered or derived, I want to emphasizethe importance of making sound justification on the collection/creation ofrelational data. For example, I reviewed a manuscript that analyzed “co-location networks” based on students’ simultaneous access to wifi hotspotson a university campus. As a critical reviewer, I would pay special atten-tion to any strong claims made on “social” connections among students, be-cause accessing a same wifi hotspot does not imply any social interaction.However, if the study looks at pairs of students simultaneously accessing 10hotspots on the campus every day, it would become a totally different storyas such intense co-location could be an indicator of (potential) social ties.Therefore, in SNA studies we need to constantly reflect on the contextualdefinition(s) of ties and the operationalization of the definitions in data col-lection.

0.11.2 Totality and sampling

In some cases, we are able to collect a whole social network. Imagine theyear-long NASA simulation of a Mars mission in an isolated dome46, re-searchers would have a better chance of studying the social network of allsix scientists in its totality.47 In other cases, when it becomes impossible tostudy a whole network (e.g., terrorist networks), researchers will need to ap-ply specific techniques of sampling.

As you will read this week, sampling in SNA research is different from sam-pling we commonly discuss in an introductory research methods course.This is because SNA research is concerned with both the nodes and the ties.Simply put, a representative sample of nodes does not naturally guaranteea meaningful sample of ties. SNA researchers need to be especially aware ofthe impact of sampling on relational data. For example, in a study we may

46https://www.theguardian.com/science/2016/aug/28/mars-scientists-nasa-dome-hawaii-mountain-isolation

47Note that the description of models introduced here may not fit the philosophicalworldview you feel comfortable with or subscribe to. Refer back to Section @ref{three-levels} for an earlier discussion we had about aligning methodology and philosophical view-points.

xlii Collect and Manage Network Data

systematically sample every 5th student from a school based on student IDs(sampling applied on nodes), and we may also ask each student to name upto 3 friends in this school (sampling applied on ties). Ego-network also im-plies an interesting sampling mechanism, as it cares about a focal ego andthe nodes to whom the ego is directly connected to plus the ties. This couldbe intuitively understood by sampling based on distance from the ego.

How we sample nodes and/or ties depends on how we specify the bound-aries of networks. The definition of network boundaries is highly criticalfor any SNA research and requires systematic considerations on researchquestions, theoretical perspectives, availability of data, etc. To quote Scott(2012):

… the determination of network boundaries is not simply a matter of iden-tifying the apparently natural or obvious boundaries of the situation underinvestigation. Although ‘natural’ boundaries may, indeed, exist, the determi-nation of boundaries in a research project is the outcome of a theoreticallyinformed decision about what is significant in the situation under investi-gation… Researchers are involved in a process of conceptual elaboration andmodel building, not a simple process of collecting pre-formed data (pp. 44-45)

This important recognition speaks back to my Week 1 video on the impor-tance of learning to make decisions in such a research methodology class.Defining the boundaries of networks is certainly the most central decisionfor an SNA project. When we start to inspect these decisions, it may lookslike we’re opening “a can of worms”, as many decisions may look artificial,or slippery at best. In this class, I hope we see decision points as “a bag ofdiamonds”—each worth staring at from different angles.48

48The sna package provides a function named ego.extract49 for the same purpose.

Ethics in SNA research xliii

0.12 Ethics in SNA research

Ethical considerations are important for both research and practice. Wewon’t spent much time on this topic this week, but I want to encourage youto attend to ethical concerns in your specific research contexts. Does yourresearch involve venerable populations (e.g., young children)? Does your re-search involve sensitive data (e.g., health data)? Is your research field onlineor offline? Because SNA is applied in all kinds of educational research, it isalmost impossible to come up with a unified ethics guideline. I strongly en-courage you to skim this chapter from an � Open Textbook� 50 produced bythe UMN Libraries. What are the possible ethical concerns in your project?I encourage you to start taking notes on how you could manage them.

I also want to mention that research ethics is never a static topic at all. Inmany emerging research spaces (e.g., the Internet), research ethics remainshighly debatable (Rivers and Lewis, 2014; Kraut et al., 2004). Feel free toshare your thoughts via Hypo by adding the ethics hashtag, or in the Slackgeneral channel.

If you’re a UMN student and wish to conduct an actual SNA project as partof the class project (which is not required), please check this UMN IRB web-site51 for further information. I’m willing to sponsor your project and we canmeet individually to talk it through.

0.13 Linear algebra basics

(You can skip this section if you’re already familiar with linear algebra.)

Matrix is all you need to know at this point. This class will focus on mathe-

50https://open.lib.umn.edu/principlesmanagement/chapter/9-5-ethical-considerations-with-social-network-analysis/

51http://www.research.umn.edu/irb/guidance/student-researchers.html

xliv Collect and Manage Network Data

matical intuitions and let the computer do heavy-lifting computations forus.

If you need a quick refresher, check out this video on matrix:

If you want to dive deeper in linear algebra, start from this intro video andmove onto its learning sequence. Again, you don’t need to watch them alland we will introduce mathematical concepts later when necessary.

0.14 Managing SNA data

On this page, I introduce recommended ways of structuring and handlingSNA data. Here I especially consider principles of tidy data (Wickham, 2014),which may question things you encounter in textbooks. The principles oftidy data are very simple (p. 4), and I will explain each principle below withexamples.

1. Each variable forms a column.2. Each observation forms a row.3. Each type of observational unit forms a table.

0.14.1 Basic representations

Note that SNA data typically include attribute data about nodes and rela-tional data about edges. So the most straightforward way to represent a net-work is to have two separate tables.

For example, consider a student group with four students (nodes). Table 1contains attribute data of each student. This table is tidy because each vari-able form a column, each observation (i.e., student) form a row, and it con-tains a single observational unit student. The third principle gets violated,for example, if you add students’ yearly test score – another observationalunit – into this table.

Managing SNA data xlv

TABLE 0.1: Table 1. A table of nodes.

name gender age

A F 15B M 14C M 13D F 14

Table 2 describes book lending activities (ties) among students. For example,Row 1 means Student A lent one book to B, while Row 4 shows B lent 2 booksto C. It is also a tidy dataset.

TABLE 0.2: Table 2. A table of weighted ties

source target weight

A B 1A C 0A D 0B C 2B D 1C D 0

Note that weight is not always required for networks. In a study that onlycares about the existence of a tie, Column 3 will contain only 0 and 1. Or,rows with having a value of 0 in Column 3 will be simply removed from thistable.

Table 3 could be the original record from which Table 2 is constructed. InTable 3, each row represents a book lending action, with its date recordedin Column 3. Here, you get a sense how researchers may need to transformdata from its original observations (Table 3) to a specific format (Table 2),even though most SNA software can handle both formats.

xlvi Collect and Manage Network Data

TABLE 0.3: Table 3. A table of raw data of ties.

source target date

A B 2017-02-03A C 2017-02-04A D 2017-02-05B C 2017-02-06B D 2017-02-07C D 2017-02-08B C 2017-02-09

Additionally, in situations you do not care about node attributes (in Table1), you can simply only use relational data – only about edges – to constructa network. In this case, you will only have a table of relational data, whichalready contain the most basic information (identifiers) of nodes. Take Ta-ble 2 for example, all unique node identifers in columns source and targetwill be extracted to create a list of nodes, with no further information abouttheir attributes.

0.14.2 Two-mode data

Imagine the research project is actually more complicated: We are also inter-ested in the relationship between book-lending behaviors and student affil-iations with sports teams. In this case, you may have two additional tablesbelow. Like what I just mentioned, you could ignore Table 4 if Table 5 alreadycontains all information about sports teams. But if there is a football teamnot covered by Table 5, you will need to include Table 6 as well.

TABLE 0.4: Table 4. Sports teams in the school.

sports_teams

baseballbasketballvolleyball

Managing SNA data xlvii

TABLE 0.5: Table 5. Student affiliation with sports teams.

student team

A basketballA volleyballB baseballC basketballD baseballD volleyball

TABLE 0.6: Table 6. Sports teams in the school (version 2).

sports_teams

baseballbasketballvolleyballfootball

Using Table 5, you could construct a two-mode network – also called as anaffiliation network – with students and sports teams as two types of actorsin the network. In contrast, Table 2 only has one mode – students.

Finally, if your research project is concerned with friendship in general– which covers both book lending and sports affiliation – you could evenmerge two types of relational data together (with solid justification). For ex-ample, from Table 5 we can tell A and C are both in the basketball team. Wecan then adjust the weight between A and B in Table 2 accordingly. This isanother type of transformation you may need to do in SNA research. Know-ing basic data transformation techniques – either in spreadsheet softwareor in R – would be helpful for work in this class.

To summarize, this page provides a basic overview of how SNA data couldbe structured. You may encounter different ways of representing SNA data,such as a relationship matrix with rows and columns representing the sameset of actors (see the Harry Potter support networks52 for example). Such

52http://www.stats.ox.ac.uk/~snijders/siena/HarryPotterData.html

xlviii Collect and Manage Network Data

representations could all be derived from a tidy dataset discussed above. Indata collection, we will strive for keeping as much raw information as pos-sible (such as timestamp), to enable analyses that only come to your mindafterwards.

0.15 Import data into software

After all these explorations in the past weeks, it’s time to play with some SNAdata and generate some graphs!!

Open Dataset: Les Miserables53, containing co-appearance weighted net-work of characters in the novel Les Miserables. (Share your thoughts on thisbook through a Hypo annotation if you’ve read it :))

Two Tracks. To accommodate your learning preferences, I provide twotracks of learning based on what SNA software you wish to learn.

• R is a statistical language that involves a little bit of coding. It may have asteep learning curve if you’ve never coded before, but I believe everyone ofus can learn it and the benefits of knowing R is huge. So I recommend Rin this course.

• Gephi is a wonderful SNA software package coming with a graphical userinterface. If you’re more comfortable with tools like MS Word or SPSS,and if you’ll never want to try R, it would be a good option for you. Thereare many similar software applications out there, many of which you’ve al-ready encountered in readings. You can use them, but they’re not officiallysupported in the class.

I’ve created two new channels R and Gephi for track-specific discussions.

53https://networkdata.ics.uci.edu/data.php?id=109

Import data into software xlix

0.15.1 Track R

If you’ve not used R before, please take Module 1 of this free course on Intro-duction to R54. If you have questions, post them in the q_and_a channel orDM Bodong.

Below are R codes to get you started (also downloadable from the #SNAEdGithub repository55). Please make sure the igraph R package is installed inyour system as it is beyond Base R. Not familiar with installing additional Rpackages, check out this video56.

You can go far beyond the codes. And make sure you share what you maketo our Slack assignment channel.

# Load igraphlibrary(igraph)

# Read datalesmis <- read.csv("https://raw.githubusercontent.com/meefen/sna-ed/master/assets/lesmis/lesmis.csv")# check the first 6 rowshead(lesmis)

# Create a graph using the graph_from_data_frame functiong <- graph_from_data_frame(lesmis)

# Plot the graphplot(g)# make the graph a little prettierplot(g, edge.arrow.size=.2, vertex.label=NA, vertex.size=8)

Below is a great video made by James Cook (a professor from University ofMaine) that would be helpful as well.

54https://www.datacamp.com/courses/free-introduction-to-r55https://github.com/meefen/sna-ed/blob/master/assets/lab_1.R56https://www.youtube.com/watch?v=u1r5XTqrCTQ

l Collect and Manage Network Data

0.15.2 Track Gephi

To begin, download the dataset here57. Open it using a spreadsheet softwareand see what’s in there. But make sure you never change anything in the file.

Follow this really nice tutorial on network visualization and analysis withGehpi. You only need to get through the first 10 minutes. Given the natureof the dataset, you may want to filter edges to leave out those edges with aweight of 0.

Like folks from Track R, please share what you make to our Slack assignmentchannel.

Have fun, everyone!!

57https://raw.githubusercontent.com/meefen/sna-ed/master/assets/lesmis/lesmis.csv

0

Sociograms and Density

In this week, we will:

• Understand how network visualization works• Become familiar with a number of network-level measures• Compute network-level measures using concrete data

An overview of Week 5 activities:

• Read and build knowledge– Carolan, ch. 5– Annotate measures with computational solutions– Identify network-level measures not covered by the book and share

to the class• Complete the data collection hands-on assignment• Compute network-level measures and share to the class

Finally, no matter whether you’re a formal or open participant of thisclass, please consider participating in a related research project. Informa-tion about this project and an electronic consent form can be found on thispage58. Your voluntary participation would be much appreciated.

58https://goo.gl/forms/M7305n1mMEF1aPWk1

li

lii Sociograms and Density

0.16 Sociograms and network visualizations

A sociogram is a graphic representation of a social network.59 Its goal is totransform mathematical representations of a network – e.g., a distance ma-trix – into a network drawing.

The creation a sociogram depends on network layout algorithms. Networklayouts are simply algorithms that return coordinates for each node in a net-work. Before the invention of such algorithms, researchers had to use graphdrawing heuristics to produce network graphs by hand, which could involvemultiple iterations of drawing. Nowadays we ask the computer to do the jobfor us :).

Decision Point. How you make a sociogram depends on what information,such as network structures and patterns, you hope to visually convey. Eventhough sociograms we’ve seen in readings are predominantly force di-rected,60 it does not mean force-directed layouts are always the best choices.

The following knowledge and understanding are important for making asociogram:62

• Know common network visualization goals (e.g., revealing segregation,showing hierarchy)

• Know network visualization types (e.g., heat maps, network maps, hiveplots), and corresponding layout algorithms

• Know visualization controls (e.g., size, color, shape, width, position)

Putting knowledge into action, when producing a sociogram you need to:

1. Identify a network visualization goal (or goals)2. Choose a network visualization type3. Apply proper visualization controls

59Note that the description of models introduced here may not fit the philosophicalworldview you feel comfortable with or subscribe to. Refer back to Section @ref{three-levels} for an earlier discussion we had about aligning methodology and philosophical view-points.

60The sna package provides a function named ego.extract61 for the same purpose.62See http://kateto.net/network-visualization

Sociograms and network visualizations liii

4. If needed, repeat 1-3.

Below, I present a few network visualization examples that do not draw onforce-directed layouts.

0.16.1 Example 1: Global Flight Network

FIGURE 1

(Source: dadaviz63)

1. Goal: Visualize patterns of the global flight network, for example,to see intensive flight activities in certain areas

2. Type: The coordinates are determined by the origin and destina-tion of each flight. In other words, no additional algorithmic deci-sions are made beyond the use of a world map.

3. Controls: Line color represents duration of a flight. Brightness ofeach line adds up to each other to represent the intensity of flightactivities in certain areas.

63http://dadaviz.com/i/2641/

liv Sociograms and Density

Note: How will this visualization look differently if the map is not eurocen-tric? Does it matter? What ‘world-views’ might have been built into such avisualization?

0.16.2 Example 2: Networks of interaction in mobile animal groups

(See the article64)

Here the concern is network dynamics, and the placement of each node (rep-resenting each individual animal) is based on its (projected) physical loca-tion in the real world.

Note: In this movie, which information naturally existed and which infor-mation was constructed by researchers?

0.16.3 Example 3: Migration Network

(Source: NYT: Where We Came From and Where We Went, State by State65)

This visualization attempts to visualize migration flows into Minnesotaacross time. This visualization could be seen as a series of ego-centric net-works of Minnesota in terms of migration into the state.

Note: Like Example 2, which information naturally existed and which infor-

64http://www.pnas.org/content/112/15/4690/F3.expansion.html65https://www.nytimes.com/interactive/2014/08/13/upshot/

where-people-in-each-state-were-born.html#Minnesota

Sociograms and network visualizations lv

mation was constructed by researchers? Which decisions did the ‘data jour-nalist’ make in this graph?

0.16.4 Example 4: Light Up the Curriculum

(See interactive version here66)

This is a visualization made to demonstrate semantic similarity amongthree types of documents—curriculum standards, students’ online posts,and their verbal discussions. This visualization technique is called hiveplots. Each axis represents a type of document. This visualization was cho-sen because researchers only cared about cross-type linkages and didn’t careabout the links within each document type.

66http://bodong.ch/assets/hive/lightup.html

lvi Sociograms and Density

0.16.5 Play more with network visualizations

This part is optional. I’m providing more materials for those who hope toexplore network visualization a bit more. Also, note that there are some “ad-vanced” concepts in these materials that we will discuss in later weeks.

Track R: I encourage you to follow this tutorial67 I’ve already mentionedabove. You can download data and R scripts used in this tutorial from theauthor’s Github repository68.

Track Gephi: I encourage you to read the first section of this tutorial69. Also,check out the following video that demonstrates Scientific Literature Analy-sis using Gephi. You are also encouraged to check out the first 3 sections ofthis Gephi tutorial70.

As always, please report back to our track-specific Slack channels – Gephiand R.

0.17 Density and Other Structural Measures for Complete Networks

Carolan (2014), chapter 571 does a great job introducing a list of commonlyused network-level measures.

Below, I make several extra points that are not covered:

First, the chapter is based on a directed, non-weighted network. We needto recognize that there are several types of networks based on the kinds ofties they have (see Table 5.172). Take the measure of density for example, thenumber of possible links are different for a directed network and an undi-rected network with the same size: a directed network has more possiblelinks because each pair of nodes have two possible links. There are different

67http://kateto.net/network-visualization68https://github.com/kateto/R-Network-Visualization-Workshop69http://kateto.net/network-visualization70http://www.martingrandjean.ch/gephi-introduction/71http://methods.sagepub.com.ezp1.lib.umn.edu/book/

social-network-analysis-and-education/n5.xml72See the R code I wrote73 to produce these toy networks.

Density and Other Structural Measures for Complete Networks lvii

algorithms (built in SNA tools) that would account for network types whencalculating these measures.

TABLE 0.7: Table 5.1: Different types of networks.

Undirected Directed

Unweighted

lviii Sociograms and Density

Undirected Directed

Weighted

Second, the researcher sometimes need to make important decisions whencomputing network measures, even if a same algorithm is applied. For ex-ample, for a weighted network, it is a common practice to set a thresh-old of weight (based on some justified reasons) to filter links weaker thanthe threshold (see Example 4 from the previous page). Then network den-sity could be computed the same way as an unweighted network. In thiscase, the calculated measure of density is highly sensible to the researcher’s

Assignments and Activities lix

decisions, which are influenced by her/his assumptions of the network.(Decision Point)

“It is important that a researcher does not use a measure simply because itis available in a standard program. A researcher must always be perfectlyclear about the assumptions involved in any particular procedure, and mustreport these along with the density measures calculated” (Scott, 2013, p. 73)

As we’re diving into specific SNA techniques – such as density, average de-gree – I want to remind you of the “3 levels of considerations” we exploredin Week 274. Decision points we’ve covered this week, such as which layoutto use and what threshold to apply when computing density of a weightednetwork, are often informed by theoretical frameworks we adopt in a studyor contextualized knowledge we have about a research problem. It is impor-tant for us to make our theoretical assumptions explicit in an SNA study.

0.18 Assignments and Activities

Due by Monday, 2/20, 11:59PM

0.18.1 Read and build knowledge

Read Carolan (2014) Chapter 575. Make Hypothesis annotations as we nor-mally do using proper hashtags (e.g., question, idea). Don’t forget to includeour SNAEd course hashtag.

Build knowledge as a group: When reading through the chapter, identify at

74https://bookdown.org/chen/snaEd/understanding-sna-in-educational-research.html

75http://methods.sagepub.com.ezp1.lib.umn.edu/book/social-network-analysis-and-education/n5.xml

lx Sociograms and Density

least one network-level measure, conduct research on how it could be com-puted using R or Gephi, and share your solution using Hypothesis. Includeat least three hashtags in your Hypothesis annotation: SNAEd, compute andR/Gephi. - If you found someone else has already covered your ‘favorite’ mea-sure, try to build on the existing solution by, for example, introducing a pa-rameter/mechanism to deal with weighted networks.

Finally, if you find a network-level measures not captured in the book, pleaseannotate HERE on this page. Briefly introduce the measure and provide acomputation technique.

0.18.2 Assignment: Data collection hands-on

As the second project checkpoint, you are required to turn in a dataset thatis organized according to the “tidy data” principles discussed last week.

• If your proposed project idea that involves human subjects and requiresan IRB approval, for this assignment you can draft a data collection planfor your project AND find a publicly available dataset to work with. If thepublic dataset you find is not tidy, you will need to transform it to a tidydataset. The Network Data Repository76 is a good place to look at, or youcan build a network based on public data (e.g., from a novel, Twitter).

– If you plan to conduct your proposed project that requires an IRBapproval, please get in touch with Bodong to work on an IRB appli-cation. This IRB webpage77 is a great starting point for you to decidewhether you need an IRB approval.

When submitting this assignment, depending on whether your dataset con-tains sensitive data or not, you can choose to share it publicly within theclass on the assignment Slack channel, or via PM to Bodong, or only sharecomputed results (more below) with the class on Slack.

76https://networkdata.ics.uci.edu/index.html77http://www.research.umn.edu/irb/research.html

Assignments and Activities lxi

0.18.3 Compute network-level measures and share

No matter which dataset you use, please try to compute network-level mea-sures and share back to the class on Slack. You are encouraged to sharescripts (for Track R) or mini-videos (for Track Gephi and R) even though theyare not required. You are also encouraged to ‘triangulate’ measures with vi-sualizations.

Enjoy a great week!

0

Centrality and Centralization

In Week 5, we explored a range of network-level measures, includ-ing size, density, diameter, average path length, centralization, reci-procity, transitivity, clustering coefficient, and so on. There are otherinteresting measures not covered by the textbook but worth your atten-tion:78

• Cohesion: The degree to which actors are connected directly to each otherby cohesive bonds.

• Structural cohesion: The minimum number of members who, if removedfrom a group, would disconnect the group.

You’ve made many great annotations on Hypothesis79. Below I’m listing afew:

1. “Six degrees of separation”

‘This was done simply for purposes of presentation; any manipulation of network datashould have some theoretical or empirical basis.’

So are ‘purposes of presentation’ valid basis for data manipulation? I am leftyearning for more explanation. – by churc25180

78Note that the description of models introduced here may not fit the philosophicalworldview you feel comfortable with or subscribe to. Refer back to Section @ref{three-levels} for an earlier discussion we had about aligning methodology and philosophical view-points.

79https://hypothes.is/stream?q=tag:snaed80https://hyp.is/vMz5hPeaEeaufPN-Sg-D0A/methods.sagepub.com.ezp1.lib.umn.edu/

book/social-network-analysis-and-education/n5.xml

lxiii

lxiv Centrality and Centralization

You might also be interested in this finding81 that “Each person … among the1.59 billion people active on Facebook … is connected to every other personby an average of three and a half other people”.

2. Theoretical basis of data manipulation

‘structural holes (one actor connected to two others who, in turn, are not connected toeach other)’

From my understanding of this, structural holes differ from triads since tri-ads generally indicate that all three actors are connected in some way. Is thiscorrect? – by tasha_mrema82

3. Usefulness of measures for specific research

‘Centralization’

Centralization interests me for analyzing discussion forums–are there keyplayers, and do these key players show higher degrees of cognitive presence?– by vbarbaro83

What are your responses to those thoughts? Please keep sharing and dis-cussing on Hypothesis + Slack.

This week, we will:

• Engage with node-level measures in social networks• Understand how network-level and node-level measures are connected

81https://research.fb.com/three-and-a-half-degrees-of-separation/82https://hyp.is/c5xSNPesEeaOSvOVuHGnBA/methods.sagepub.com.ezp1.lib.umn.edu/

book/social-network-analysis-and-education/n5.xml83https://hyp.is/aNW93vbhEea-vRvbw4TlvQ/methods.sagepub.com.ezp1.lib.umn.edu/

book/social-network-analysis-and-education/n5.xml

Centrality and Centralization: An Overview lxv

• Learn to calculate node-level measures using SNA applications

Again, no matter whether you’re a formal or open participant of this class,please consider participating in a related research project. Informationabout this project and an electronic consent form can be found on thispage84. Your voluntary participation would be much appreciated.

0.19 Centrality and Centralization: An Overview

When we consider the importance of a node in a social network, how centralit is usually an important consideration. In Week 4, we were able to use so-ciograms to identify central nodes in a network. How can we identify thosecentral nodes mathematically in case they are not easily visually identifiable?

Centrality is a key measure in SNA developed to achieve this goal. SNA re-searchers have developed many ways to quantify centrality in a network. Be-low, I curate a list of quality resources for you to explore different central-ity measures. I selected these resources because of varied ways they presentcentralities – equations vs. intuitions, real-world examples vs. toy networks,step-by-step demonstrations vs. one-step computation.

First, review the following PDF presentation85 presenting four main cen-trality measures: Degree Centrality, Betweenness Centrality, ClosenessCentrality, and Eigenvector Centrality. Note that the author introducesnode-level centrality and network-level centralization together in thispresentation. These two concepts are often mistakenly treated as the sameby researchers. Now you see their differences and connections. Also, if youcould follow the math equations, that would be great; if not, please focus onthe intuitions.

Second, watch the following video from Lada Adamic covering Degree Cen-trality, Betweenness Centrality, and Closeness Centralitywith concreteexamples. She also made an attempt to distinguish centralities from central-ization. She also noted that when considering centrality, it is very important

84https://goo.gl/forms/M7305n1mMEF1aPWk185http://www.stat.washington.edu/~pdhoff/courses/567/Notes/l6_centrality.pdf

lxvi Centrality and Centralization

to be clear about the scope, or the boundary like we discussed in Week 0.10.2.A little tweak will make a difference.

0.20 Betweenness Centrality

Diving deeper, betweenness centrality is probably the most popular cen-trality measure I’ve personally seen in educational research. The notion ofresiding in-between has strong implications for many scenarios, either for fa-cilitating/blocking access to resources or encouraging creativity. So I thinkbetweenness centrality is worth further exploration.

Below is a great video made by James Cook to explain betweenness central-ity. Enjoy!

0.21 Eigenvector Centrality

Eigenvector centrality is another centrality measure that is well alignedwith the social capital theory. Watch the following video by Lada to find outmore.

0.22 Week 6 Activities

0.22.1 Readings

None. The textbook does not provide a specific introduction to centraly mea-sures for a whole network.

But you’re encouraged to look back into example papers you selected inWeek 3 to see whether you’ve developed any fresh understanding after div-

Week 6 Activities lxvii

ing deeper into these measures. Please share your findings with the class onSlack.

0.22.2 Compute Node-level Measures

0.22.2.1 Track R

Search “centrality” on the igraph doc page86. For example, you will find thatbetweenness(g) is the function for computing betweenness centrality. Applythese centrality functions on your dataset from Week 5. Tweak the parame-ters, such as directed, to see how the results might change. Share your find-ings on Slack.

0.22.2.2 Track Gephi

Some of you have already played with Gephi’s Statistics panel in Week 4. Forthis week,

• Check page 12 of this Gephi tutorial87 to see how centralities could be com-puted using Gephi. See Figure 2.

• Toggle to Data Laboratory to see results of Gephi computations in the DataTable tab. For example, if you click on Network Diameter in the Statisticspanel, a number of centrality measures (including betweenness centrality)will be saved in the Data Table. You can click on the header of each columnto sort the Data Table. See Figure 3.

• Share your findings on Slack.

Like earlier weeks, if you have any questions or ideas, share in correspond-ing channels on Slack. Enjoy a great week!

86http://igraph.org/r/doc/87https://gephi.org/tutorials/gephi-tutorial-quick_start.pdf

lxviii Centrality and Centralization

FIGURE 2: Gephi Graph Overview.

FIGURE 3: Gephi Data Laboratory.

0

Components and Cliques

Our goals for Week 7 include:

• Understanding components and cliques• Becoming familiar with several popular approaches to identifying groups• Using SNA software to identify components and detect cliques

0.23 Introduction to Components and Cliques

Please watch the following video before reading Chapter 688 of Carolan(2014). This video provides intuitions that could be useful before diving intomathematical representations.

0.24 From Data to Analyses: A Demo

In the following video, I demonstrate a process of going from a secondarydataset towards some simple analyses covered in the past few weeks. Thisdemo is especially useful if you are in Track R. But some principles, such astidy data and reproducible analysis, should also apply for Track Gephi.

R code used in this demo can be found here89. Please feel free to reuse andextend.

88http://methods.sagepub.com.ezp1.lib.umn.edu/book/social-network-analysis-and-education/n6.xml

89https://github.com/meefen/sna-ed/blob/master/assets/lab_week7.R

lxix

lxx Components and Cliques

0.25 Assignments and Activities

0.25.1 Read, Annotate, and Share

• Read Carolan (2014), ch. 690

• Annotate as we normally do using proper hashtags (e.g., question, idea).Don’t forget to include our SNAEd course hashtag.

• Share tips and tricks related to component/clique analysis on Slack:– For Track R, post Code Snippets from your analysis on the R channel.

You can post anything that others may find useful. For example, youcan show off your code that detects strong components in a directednetwork.

– For Track Gephi, post description, snapshots, or posts on the Gephichannel.

• (Optional) Find and Share an educational study that deals with networkcomponents or cliques. Point out specific techniques applied in that study.

• Don’t forget to respond to each other’s contributions!

0.25.2 Project Checkpoint 2

In this week, there is a project checkpoint assignment designed to keep you“on track”. The description of this checkpoint reads as following:

Students will share their refined project ideas, with a concrete data collec-tion plan fleshed out.

At this point, we have diverged tremendoulsy on the final projects! I under-stand that you are all at different stages of your projects and some of youare dealing with IRB applications. So I will not require formal submission

90http://methods.sagepub.com.ezp1.lib.umn.edu/book/social-network-analysis-and-education/n6.xml

Assignments and Activities lxxi

of this assignment and instead encourage you to make an appointment withme to discuss your project if needed.

Have a great week!

0

Ego-centric Networks

In the past three weeks, we explored a wide range of concepts and measuresfor analysis of whole networks, sub-networks (or sub-graphs), and individualnodes. This week, we will dive into ego-centric networks as a very unique ap-proach to SNA. Specifically, we will:

• Understand what is an ego-centric network• Understand different levels of ego-centric networks• Understand how ego-centric network data can be collected• Develop initial ideas of applying ego-centric networks in educational set-

tings

In the previous week, I enjoyed reading your Hypothesis annotations and in-teractions. I especially appreciate your efforts in connecting concepts acrossweeks, and connecting concepts with your own work. For example, Ramyaasked91 about the connection between cutpoints and network cohesion; Tinarecognized92 similarities between cutpoints and bridges; Derek pointed out93

several important decisions we need to make when applying concepts in aparticular context. These are all great and thanks for engaging each otherin diving deeper in these areas! Please watch the video below to get startedwith Week 8:

91https://hyp.is/_HHwJv1nEean4-OGO81R9A/methods.sagepub.com.ezp1.lib.umn.edu/book/social-network-analysis-and-education/n6.xml

92https://hyp.is/_HHwJv1nEean4-OGO81R9A/methods.sagepub.com.ezp1.lib.umn.edu/book/social-network-analysis-and-education/n6.xml

93https://hyp.is/oyDt5AA_Eee_lBskXThq7Q/methods.sagepub.com.ezp1.lib.umn.edu/book/social-network-analysis-and-education/n6.xml

lxxiii

lxxiv Ego-centric Networks

0.26 Introduction to Ego-Centric Networks

Egocentric analysis shifts the analytical lens onto a sole ego actor and con-centrates on the local pattern of relations in which that ego is embedded aswell as the types of resources to which those relations provide access. (Car-olan, 2014, ch. 7)

The concept of ego-centric networks is pitched against socio-centric networks thatwe’ve been exploring so far in this class. Some researchers also refer to ego-centric networks as ego networks or personal networks. These two types of net-works are distinct in several important ways (Perry, n.d.94):

• Unbounded versus bounded networks. Sociocentric SNA collects data onties between all members of a socially or geographically-bounded groupand has limited inference beyond that group. Egocentric SNA assesses in-

94https://www.icpsr.umich.edu/icpsrweb/sumprog/courses/0213

Introduction to Ego-Centric Networks lxxv

dividuals’ personal community networks across any number of social set-tings using name generators, and is therefore less limited in theoreticaland substantive scope.

• Focus on individual rather than group outcomes. Sociocentric SNA oftenfocuses on network structures of groups as predictors of group-level out-comes (e.g. concentration of power, resource distribution, information dif-fusion). In contrast, egocentric SNA is concerned with how people’s pat-terns of interaction shape their individual-level outcomes (e.g. health, vot-ing behavior, employment opportunities).

• Flexibility in data collection. Because sociocentric SNA must use as its sam-pling frame a census of a particular bounded group, data collection is verytime-consuming, expensive, and targeted to a specific set of research ques-tions. In contrast, because egocentric SNA uses individuals as cases, poten-tial sampling frames and data collection strategies are virtually limitless.Egocentric data collection tools can easily be incorporated into large-scaleor nationally-representative surveys being fielded for a variety of other pur-poses.

Ego-centric networks are useful when the foci of the research are individu-als in a network, if capturing the complete network is less important, and/orwhen the researcher plan to correlate attribute data of individuals with theirrelational characteristics in a network. Examples of ego-centric networks’ ap-plications abound. As we explored in Week 395, ego-centric networks can beused to investigate stroke patients’ health behaviors. In education, for ex-ample, Dawson (2010) studies high and low-performing students based ontheir ego-networks.

Below, James Cook – a sociology professor we’ve been watching – nicely ex-plains how studying ego-centric networks would be helpful.

How ego-centric networks could be applied to your research projects? Youdo not necessarily need to focus on your class project but projects in yourfield in general.

95https://bookdown.org/chen/snaEd/applications-and-examples-of-sna.html

lxxvi Ego-centric Networks

0.27 Collecting Ego-Centric Data

As you’ll read in our textbook, there are basically two ways to construct ego-centric networks:

1. Ego-centric networks by design: When a research project is initi-ated by asking ego-centric questions, ego-centric data are usuallydirected collecting. For example, when a name generator question-naire is distributed to a sample of students in a large high schoolto study in-school friendship of students, each student’s responsewill be directly used to construct a network.

2. Derived ego-centric networks: When a complete network can becaptured, we can also derive ego-centric networks by filtering net-work data. For example, if we’re analyzing our own Slack discus-sions, we can also create an ego-centric network for each one ofus to investigate our connectedness in the class.

In either of these conditions, an important decision to make is how you de-fine the neighborhood of the ego-centric network, or how many steps doesan ego can reach, as Cook explored in his video. This will again be informedby theories and contextual information you bring to bear. [Decision Point]

What definition of the neighborhood will make sense for your researchprojects?

0.27.1 “Les Miserables” Example

Below I demonstrate the difference between one-step vs. two-step ego net-works using the “Les Miserables” dataset96 we played with earlier. Whichtype of ego networks would make more sense for analyzing characters inthis novel?

96Note that the description of models introduced here may not fit the philosophicalworldview you feel comfortable with or subscribe to. Refer back to Section @ref{three-levels} for an earlier discussion we had about aligning methodology and philosophical view-points.

Collecting Ego-Centric Data lxxvii

First, explore one-step ego networks by choosing or clicking on a node:

Second, two-step ego networks:

lxxviii Ego-centric Networks

0.28 Analyzing Ego-Centric Networks

In the textbook, the author explores a range of measures that we’ve intro-duced when studying complete networks, such as density and centrality. Thisis another chance to examine these concepts even though computing thesemeasures is the same mathematically for complete or ego networks.

In this week, I encourage you to use a complete-network dataset you have inhand (e.g., your own data, demo data we used in earlier weeks, Twitter dataI demoed) to:

Analyzing Ego-Centric Networks lxxix

• Derive ego-centric networks based on a complete network• Conduct basic analysis of ego-centric networks

0.28.1 Track R

This igraph doc97 is where you can get started. Play with different parame-ters to see how results could be different.

Additionally, explore ways to extract ego networks from the complete net-work using the make_ego_graph() function.98

Note: If you haven’t done so yet, please the video I made in Week 7. Youcan add new code dealing with ego-centric networks in to your earlier code.(This is when you’re starting to love R if the past few weeks were a bit rough:).)

0.28.2 Track Gephi

The half-minute video below will give you a sense about steps involved inderiving ego-centric networks from a complete network:

Additionally, there are a number of posts that provide more detailed guid-ance:

• gephi: Centring a graph around an individual node100

• My Facebook Network, Part III: Ego Filters and Simple Network Stats101

• Page 3 of Introduction to Network Analysis: Working with Gephi (pdf)102

Optional if you’re using Windows:

• UCINET103 provides good support for ego-centric network analysis. Youcan find a detailed tutorial here104.

97http://igraph.org/r/doc/ego.html98The sna package provides a function named ego.extract99 for the same purpose.

100http://www.markhneedham.com/blog/2012/04/30/gephi-centring-a-graph-around-an-individual-node/101https://blog.ouseful.info/2010/05/10/getting-started-with-gephi-network-visualisation-app-%

E2%80%93-my-facebook-network-part-iii-ego-filters-and-simple-network-stats/102https://introdh.files.wordpress.com/2011/10/gephi-workshop-01.pdf103https://sites.google.com/site/ucinetsoftware/home104http://www.faculty.ucr.edu/~hanneman/nettext/C9_Ego_networks.html

lxxx Ego-centric Networks

• E-Net105 is an SNA tool specially designed for ego network analysis. Hereis An Introduction to Personal Network Analysis and Tie Churn Statisticsusing E-NET106. You can also find public datasets107 from its website.

0.29 Week 8 Activities

1. Read Carolan (2014), ch. 7108. Annotate as we normally do usingproper hashtags (e.g., question, idea).

2. Respond below to two questions raised in Sections 0.26 and 0.27via Hypothesis annotations. Discuss among each other via Hy-pothesis to make suggestions, expand ideas, explore collabora-tion, etc. Don’t forget to include our SNAEd course hashtag or otherhashtags deemed relevant.

•How ego-centric networks could be applied to your researchprojects?

•What definition(s) of the neighborhood will make sense foryour research projects?

3. Post results of your ego-centric network analysis in the assign-ment Slack channel. For both R and Gephi tracks, you can chooseto either (1) focus on one ego in your network, or (2) derive egonetwork measures and/or visualizations for every node in the net-work. When sharing, please make a Slack Post instead of postingmultiple messages.

Have a wonderful week!

105https://sites.google.com/site/enetsoftware1/106https://50e20782-a-62cb3a1a-s-sites.googlegroups.com/site/enetsoftware1/

files/Halgin%20%26%20Borgatti%202012%20Personal%20Network%20Analysis.pdf107https://sites.google.com/site/enetsoftware1/datasets108http://methods.sagepub.com.ezp1.lib.umn.edu/book/

social-network-analysis-and-education/n7.xml

0

Applications and Examples II

In Week 0.8.2, we explored a range of example applications of SNA in educa-tion. The purpose of that exploration was to expose ourselves to the poten-tial of SNA for educational research and to get acquainted with basic SNAterminologies that were later introduced in the course.

This week, after considerable work on several areas, we’re going to do a ‘deepdive’ in more examples. This time, you are bringing with yourself an ‘arsenal’of SNA concepts and techniques. By critically examining examples closely,the goal of this week’s exploration is to further:

• Understand how an SNA study could become theoretically and method-ologically aligned

• Detect critical decisions of SNA research in action• Understand how SNA techniques could be combined with other methods

Please watch the introduction video below to get started:

0.30 Week 9 Activities

• Read, Examine & Share, due by Sunday March 26, 11:59PM• Comment, due by Monday March 27, 11:59PM

0.30.1 Read, Examine & Share

Choose: A research article that is/seems highly relevant to your project idea(a list is offered below if you cannot identify one by yourself). Record its bibli-ographic information so that you can share with the class. Ideally this article

lxxxi

lxxxii Applications and Examples II

could serve as a model text for your ‘Project Final Artifact’, especially if youplan to develop something publishable from this course.

Examine this article closely, focusing on the following areas: 1) research pur-poses served by SNA in the study; 2) specific SNA techniques applied; 3) howSNA is combined with other methodology.

Share your thoughts as a Slack Post on the assignments channel. In this post,add key take-aways from this article that may inform your own researchproject. This Slack post is due by Sunday March 26, 11:59PM.

0.30.2 Comment

Spend time reading each others’ posts. When you’re reading, try your best to‘borrow’ ideas from articles introduced by others to inform your own project.Make sure you credit a colleague’s contribution to your thinking by com-menting on her post.

Please try to comment on at least 2 classmates’ posts. Comments are due byMonday March 27, 11:59PM.

0.30.3 Lists of articles to choose from

Note: Ideally you will choose a reading by yourself that is pertinent to yourproject idea.

Examples from LAK17

• Boroujeni, M. S., Hecking, T., Hoppe, H. U., & Dillenbourg, P. (2017). Dy-namics of MOOC discussion forums. In Proceedings of the Seventh Inter-national Learning Analytics & Knowledge Conference on - LAK ’17 (pp. 128–137). New York, New York, USA: ACM Press. https://doi.org/10.1145/3027385.3027391

• Poquet, O., Dawson, S., & Dowell, N. (2017). How Effective is YourFacilitation?: Group-level Analytics of MOOC Forums. In Proceedingsof the Seventh International Learning Analytics & Knowledge Confer-ence (pp. 208–217). New York, NY, USA: ACM. https://doi.org/10.1145/3027385.3027404

Week 9 Activities lxxxiii

• Wise, A. F., Cui, Y., & Jin, W. Q. (2017). Honing in on social learning net-works in MOOC forums: examining critical network definition decisions.In Proceedings of the Seventh International Learning Analytics & Knowl-edge Conference (pp. 383–392). ACM. https://doi.org/10.1145/3027385.3027446

List of articles from Week 3

• Daly, A. J., & Finnigan, K. S. (2011). The Ebb and Flow of Social NetworkTies Between District Leaders Under High-Stakes Accountability. Ameri-can Educational Research Journal, 48(1), 39–79.

• Baker-Doyle, K. (2010). Beyond the Labor Market Paradigm: A Social Net-work Perspective on Teacher Recruitment and Retention. Education PolicyAnalysis Archives, 18, 26.

• Heck, R. h., Price, C. l., & Thomas, S. l. (2004). Tracks as Emergent Struc-tures: A Network Analysis of Student Differentiation in a High School.American Journal of Education , 110(4), 321–353.

• González Canché, M. S., & Rios-Aguilar, C. (2015). Critical Social NetworkAnalysis in Community Colleges: Peer Effects and Credit Attainment. NewDirections for Institutional Research, 2014(163), 75–91. https://doi.org/10.1002/ir.20087

• Hill, M. (2002). Network Assessments and Diagrams: A Flexible Friend forSocial Work Practice and Education. Journal of Social Work , 2(2), 233–254.

• Christley, R. M. (2005). Infection in Social Networks: Using Network Anal-ysis to Identify High-Risk Individuals. American Journal of Epidemiology,162(10), 1024–1031. http://doi.org/10.1093/aje/kwi308

• Christakis, N. A., & Fowler, J. H. (2007). The spread of obesity in a largesocial network over 32 years. The New England Journal of Medicine, 357(4),370–379.

• Dawson, S., Tan, J. P. L., & McWilliam, E. (2011). Measuring creative poten-tial: Using social network analysis to monitor a learners’ creative capacity.Australasian Journal of Educational Technology, 27(6), 924–942.

• Honeycutt, T. (2009). Making Connections: Using Social Network Analysisfor Program Evaluation. Mathematica Policy Research, (1), 1–4.

• Rienties, B., Héliot, Y., & Jindal-Snape, D. (2013). Understanding sociallearning relations of international students in a large classroom using so-cial network analysis. Higher Education, 66(4), 489–504. http://doi.org/10.1007/s10734-013-9617-9

lxxxiv Applications and Examples II

• Martinez, A., Dimitriadis, Y., Rubia, B., Gómez, E., & de la Fuente, P. (2003).Combining qualitative evaluation and social network analysis for the studyof classroom social interactions. Computers & Education, 41(4), 353–368.

• Roberson, Q. M., & Colquitt, J. A. (2005). Shared and Configural Justice: ASocial Network Model of Justice in Teams. Academy of Management Re-view. Academy of Management, 30(3), 595–607.

0.31 Course Project Check-in

Based on our Slack communications (public or private), you are all makingprogress on your course projects. I want to make a few notes so that you canplan your project:

• The Project Final Artifact is worth 30 points. Each student will produce aproject final artifact that represents preliminary results of their initialproject ideas. The specific format of this artifact, which could be a researchpaper, an e-portfolio, or an interactive tool, is to be negotiated in advancewith the instructor. If you have ideas/concerns with your own project,please send Bodong a Direct Message.

• A rubric will be shared next week to guide your work on the Project FinalArtifact. But do use this week’s exploration as an opportunity to make anoutline for your Final Artifact. As I’ve mentioned in earlier weeks, I’m look-ing for your capabilities in making theoretically and methodologically in-formed decisions in a research area you specialize.

• If you are still waiting for your data to come in and haven’t done SNA anal-yses in the past few weeks, I strongly suggest you watch this video in Week7109. The idea is for you to practice SNA techniques use a toy dataset, andplug in your own dataset when it is ready. (This is the charm of R and re-producible research.)

109https://bookdown.org/chen/snaEd/from-data-to-analyses-a-demo.html

Course Project Check-in lxxxv

0.31.1 Use an R Notebook

I mentioned this tip in an earlier video, and want to mention it again thatif you’re using R/igraph for your SNA project, please keep a file (or multiplefiles) containing your R scripts. You can directly compile a new report afteradding new scripts to your growing project each week. You can reuse yourscripts for a new dataset. You can … I can go on for another 1,000 words,but the key idea is your project (containing your ideas, data, scripts) is fullyrecorded and reproducible.

To learn more about R Notebooks, check out the video below. Note that youcan (1) compile a report directly from a .R file, and (2) compile a report froma .Rmd (i.e., R Markdown110) file.

Again, if you have specific questions, post them on the q_and_a channel orreach me via Slack PMs. If you think the questions are too complicated, bookan appointment with me via http://bit.ly/bookchen

Have a wonderful week!

110http://rmarkdown.rstudio.com/

0

Statistical Analysis with Network Data

In his book, John Scott (2012) commented on a struggle shared among manyresearchers – including many of us – who are attracted to SNA because ofspecific analytical needs but get turned away by SNA’s mathematical andstatistical complexity. The most central goal of this course is to address thischallenge, by focusing on essential SNA concepts – e.g., density, centrality,cliques, etc. – instead of the nitty-gritty mathematical details involved inSNA, so that we feel confident in designing an SNA study and venturinginto numerous directions made possible by SNA (and network analysis ingeneral).

This week, we will stretch to statistical analysis with network data that mayunleash the power of work you’ve been doing so far. In particular, we willwork to:

• Understand differences between the mathematical and statistical ap-proaches to SNA

• Become familiar with different kinds of statistical analysis with networkdata

• Plan on applying statistical modeling approaches to your SNA project (ifpossible)

0.32 Introduction

The video at the bottom provides an introduction to this week.

Before this video, I want to mention that statistical models and modeling willget mentioned quite frequently in this week’s text. These terms are centralto statistics in general. What a model does is to provide a statistical approx-

lxxxvii

lxxxviii Statistical Analysis with Network Data

imation of the ‘reality’ we are interested, so that by generating ‘better’ ap-proximations we are essentially getting closer to truly understanding the‘reality’.111 I personally like a point made by (Burnham and Anderson, 2003)that all models are essentially wrong:

Fundamental to our paradigm is that none of the models considered as thebasis for data analysis are the ‘true model’ that generates the biological datawe observe… A model is a simplification or approximation of reality andhence will not reflect all of reality (p. 20)

0.33 Week 10 Activities

1. Read Carolan (2014), ch. 8112 and ch. 9, till the end of Regression113.

2. Annotathon on our Carolan textbook website. Because this week’stopic is of great complexity, we’re going to rely on our collectivewisdom to develop deeper understanding. So please post yourquestions, examples, resources, scripts, and so on as Hypothesisannotations when reading the textbook.

3. Post on Slack a brief report from your project involving at least onestatistical analysis we’ve discussed this week (e.g., t-tests, ANOVA,regression, ERGMs).

• Many of you appreciated seeing each other’s reports that include scripts

111Note that the description of models introduced here may not fit the philosophicalworldview you feel comfortable with or subscribe to. Refer back to Section @ref{three-levels} for an earlier discussion we had about aligning methodology and philosophical view-points.

112http://methods.sagepub.com.ezp1.lib.umn.edu/book/social-network-analysis-and-education/n8.xml

113http://methods.sagepub.com.ezp1.lib.umn.edu/Book/social-network-analysis-and-education/n9.xml

Course Project Check-in lxxxix

and results. And I myself will also post a report to our community space(i.e. Slack) later this week.

• If you are using R, please check last week’s notes on using an R Notebook114

for report generation.• If you are using Gephi, you do not have as many options as R provides. But

you can export your network data populated with network measures to anexternal statistical software (e.g., SPSS) for additional analysis.

0.33.1 Additional resources

• Kolaczyk and Csárdi (2014)• Snijders (2011)• Apkarian and Hanneman (2016) – link115

0.34 Course Project Check-in

Below is a rubric you can follow while working on your course project. Eachcomponent is of equal weight and needs to be addressed in your project ar-tifact.

If you propose a different format – such as an interactive SNA tool for a spe-cific audience – please get in touch with Bodong to discuss an adapted rubricthat will work for you.

114https://bookdown.org/chen/snaEd/course-project-check-in.html#use-an-r-notebook

115http://www.annualreviews.org.ezp1.lib.umn.edu/doi/10.1146/annurev.soc.012809.102709

xc Statistical Analysis with Network Data

Components 4-Expert 3 2 1-Novice

Statement ofthe problem,grounding inthe literature

Very wellwritten. Setsup andarticulates aninterestingproblem thatis groundedwithin alarger context.Provides aconcise,thoughtfulstatement ofthe problemand its broadsignificance.

Shows afundamentallack of under-standing ofthe problem.Poorlywritten,incomplete,lacksstructure.

Crafting ofresearchquestions

Clearly stated,concreteresearchquestion(s)developed toaddress thestatedproblem.Questions arespecific,answerable,andconceptuallysignificant.

Questions aretoo vague,broad, orinsignificant.

Course Project Check-in xci

Components 4-Expert 3 2 1-Novice

Methodology Properly usesSNA and itstechniques toanswerresearchquestions.Design ofstudy showsstrong graspof importantresearchdecisions inSNA. Propercombinationof SNA withother method-ologies whennecessary.Network dataare managedandtransformedproperly.

Uses SNAincorrectly,eitherbecause of alack of under-standing ofspecificmethods ormis-alignmentbetweenmethods andresearchquestions.Network dataare nothandledappropriately.

Analysis,results, andinterpretation

Promisingresultsobtainedfrom dataanalyses.Analyses mapback to thequestionsinsightfully.Discusses thelimitations ofthe analysis.

Mis-analyzesdata or failsto analyzerelevant data.Results do notfollow fromthe analysisand mistakesare made ininterpretation.

xcii Statistical Analysis with Network Data

Components 4-Expert 3 2 1-Novice

Formatting,documenta-tion ofsources, andreproducibleresearch

Citations andreferencesfollow theAPA Style.Use properheadings andsubheadingsconsistently.Include aconciseabstract andkeywords. Aplus ifanalysisscripts andresults areseamlesslyintegrated(e.g., as an RNotebook) tosupportreproducibleresearch.

No or missingreferences.Headings andsubheadingsinconsistentor absentaltogether.Missingabstract orkeywords.

Have a great week!

0

Network Dynamics and Temporality

It’s About Time!

So far in this class we’ve been mostly working with staticnetworks or snap-shots of dynamic networks. That’s enough for most of our needs. However,social networks are dynamic in nature. One important use of SNA is to un-derstand how an network would function given its current structure. Sucha question is genuinely about network dynamics.

In Week 11, we will:

• Explore ways to conceptual time and temporality in SNA• Learn how to construct temporal networks• Learn approaches to visualizing and measuring temporal networks• Explore potential application of temporal SNA to our projects

Note: You may see people using different words temporal, dynamic, longitudi-nal interchangeably to describe social networks.

0.35 Class Google Hangout

If you missed our class Hangout, or you could only attend a part of it, pleasecheck the recording that has been shared via Slack announcement. The record-ing was set as private so please make sure you are signed in with your UMNGoogle account.

xciii

xciv Network Dynamics and Temporality

Reflection: It was fun to get together. But attending to two spaces – F2F andonline – in the same time was challenging to me. Many thanks to Nic andWeiyi for your patience!

Week 11 materials have been posted here:

• Slides116

• The demo with R code117 (if you see random text, please save the file to yourcomputer and open it again)

0.35.1 Tools for temporal network analysis

Gephi supports the analysis of dynamic networks. This website, ExploringBig Historical Data118, provides a useful introduction. See also the Youtubevideo below.

R packages networkDynamic, tsna, and ndtv are very useful for temporal net-work analysis and visualization.

0.36 Week 11 Activities and Upcoming Milestones

0.36.1 Week 11 activities

Our textbook does not have a chapter on this topic, but you’re encouragedto explore resources and examples of temporal SNA by yourself and shareback to our class via either Slack or Hypothesis.

Below are a few readings you can start with:

• Gloor et al. (2004)• Jiang et al. (2013)• Myllari et al. (2010)• Rodriguez et al. (2014)

116https://github.com/meefen/sna-ed/blob/master/assets/ch11.md117https://raw.githubusercontent.com/meefen/sna-ed/master/assets/temporal.html118http://www.themacroscope.org/2.0/dynamic-networks-in-gephi/

Week 11 Activities and Upcoming Milestones xcv

• Raghavan et al. (2014)• Carley et al. (2014)

The Network Analysis Hands-on is due on 4/10. Please turn in a more-or-lesscomplete version of your ongoing project. Basically this is another check-inpoint to keep you on track and for you to receive additional feedback.

0.36.2 Upcoming milestones

To reiterate, there are three upcoming milestones:

• 4/10, Network analysis hands-on• 5/1, Project presentations – I will send out another quick Doodle poll to set

a date and time.• 5/8, Project final artifact + Reflection essay due – You can find some basic

info on the syllabus. More detailed info will be shared in later weeks.

Have a wonderful week!

0

Planning SNA Research and Projects

As we are all deeply immersed in the course project, in this week instead ofexploring “Novel Approaches and Analytics” as planned in the syllabus, wewill be reflective and continue to refine our projects. Hopefully this changewill help you better focus on your projects, and we will come back to explorecool SNA approaches next week.

0.36.3 Week 12 activities

1. Read Carolan (2014), Chapter 12119. This chapter summarizesmany things we’ve already been doing in this class, and couldserve as a good resource for you to self-check your ongoing workon the course project.

2. Annotathon on our Carolan textbook website using Hypothesis.Below are four prompts:

• When reading through the nine steps presented in this chapter, annotateareas where your project is currently falling a little bit short or will benefitmore work from.

• When reading through the nine steps, annotate things you will do differ-ently from the author.

• When reading through the Software Sampler, annotate software packagesyou wish to try in the future and explain why. Please share useful resourcesyou found to the class.

• On Research Ethics, share any thoughts you have about ethical considera-tions in SNA research and practice.

119http://methods.sagepub.com.ezp1.lib.umn.edu/book/social-network-analysis-and-education/n12.xml

xcvii

xcviii Planning SNA Research and Projects

As always, please add our SNAEd tag, and other appropriate tags, to your Hy-pothesis annotations.

3. Continue to refine your SNA projects. If you have questions,please post them in the Slack q_and_a channel or directly PMBodong.

0.36.4 Upcoming milestones

As a reminder, we have two upcoming milestones:

• 5/1, Project presentations – I will send out another quick Doodle poll to seta date and time.

• 5/8, Project final artifact + Reflection essay due – You can find some basicinfo on the syllabus. More detailed info will be shared in later weeks.

Have a wonderful week!

0

Novel Approaches and Analytics

As we are coming to the final two weeks of this course, I hope we are allcoming to appreciate the power of SNA and the relational perspective ingeneral. It is totally fine if you are ‘still’ wrestling with certain areas of SNA,as every one of us brings unique background into this course and may ei-ther need extra time to grasp certain concepts/techniques or wish to engagemore deeply with certain areas. As the instructor, I will be most happy if thiscourse would serve as a starting point for your journey with SNA.

SNA and network analysis in general are constantly evolving. The potentialto apply SNA is endless. This week, we will explore some “unusual” use ofSNA and, in some cases, a combination of SNA with other techniques. Pleasewatch the video to get started.

Note: I was unable to introduce activities in the video. Please proceed to thenext page for detailed information, which should be fairly straightforward.

0.37 Resources and Activities

In this week, each of us will:

1. Identify/select a novel SNA-based approach, technique or tool2. Review and critique the choose approach or tool for our class

xcix

c Novel Approaches and Analytics

0.37.1 Resources

You have absolute freedom in choosing a novel SNA-based approach, tech-nique or tool. Below I provide a list of ‘candidates’ based on my areas of in-terest, which may not overlap with yours.

When making your choice, you should have a vague idea about what ‘novelty’means to you. There is no standards to judge novelty in this course but itwould be helpful if you can somehow justify your choice.

• Shaffer, D. W., Hatfield, D., Svarovsky, G. N., Nash, P., Nulty, A., Bagley,E., … Mislevy, R. (2009). Epistemic Network Analysis: A Prototype for 21st-Century Assessment of Learning. International Journal of Learning andMedia, 1(2), 33–53. https://doi.org/10.1162/ijlm.2009.0013 (Note: A novelnetwork analysis tool developed to analyze high-order competencies.)

• Carley, K. M., Pfeffer, J., Morstatter, F., & Liu, H. (2014). Embassiesburning: toward a near-real-time assessment of social media using geo-temporal dynamic network analytics. Social Network Analysis and Mining,4(1), 195. https://doi.org/10.1007/s13278-014-0195-3 (Note: A collection oftools that extract network data from fairly free-form social media data.)

• Ryu, S., & Lombardi, D. (2015). Coding Classroom Interactions for Collec-tive and Individual Engagement. Educational Psychologist, 50(1), 70–83.http://doi.org/10.1080/00461520.2014.1001891 (Note: An attempt to com-bine SNA with critical discourse analysis.)

• Oshima, J., Oshima, R., & Matsuzawa, Y. (2012). Knowledge Building Dis-course Explorer: A social network analysis application for knowledge build-ing discourse. Educational Technology Research and Development, 60(5),903–921. http://doi.org/10.1007/s11423-012-9265-2 (Note: A novel tool de-veloped for the analysis of discourse data, esp. by combining social and semantic as-pects together.)

• Andrade, A. (2015). Using Situated-Action Networks to visualize complexlearning120. In O. Lindwall, P. Hakkinen, T. Koschmann, P. Tchounikine,& S. Ludvigsen (Eds.), Exploring the Material Conditions of Learning: TheComputer Supported Collaborative Learning (CSCL) Conference 2015, Vol-ume 1 (pp. 372–379). Gothenburg, Sweden: International Society of theLearning Sciences. (Note: A theory-driven approach to develop a new network-based analytical approach.)

120https://www.isls.org/cscl2015/papers/MC-0340-FullPaper-Andrade.pdf

Resources and Activities ci

• SNAPP (Social Network Analysis & Pedagogical Practices)121 (Note: One so-cial network analytic tool that can be directly layered on top of discussion data insome LMSs for real-time SNA.)

• …

0.37.2 Reflect and Share

After spending time with resources related to the identified SNA-based in-novation, you are expected to reflect on a few aspects:

1. Which traditional SNA techniques are reflected in this innova-tion?

2. Which ‘cool’ or ‘novel’ elements are introduced by this innovationcompared to traditional SNA?

3. Which practical and/or scholarly value does this innovation intro-duce?

Post your reflection on the Slack assignment channel. A mini video presen-tation is preferred this time so that you’re warming up for our final projectpresentations.

Have fun and I look forward to learning from your explorations!

121https://confluence.sakaiproject.org/pages/viewpage.action?pageId=84902193

Bibliography

Apkarian, J. and Hanneman, R. A. (2016). Statistical Analysis of Social Networks.City University of New York, York College, Jamaica, NY.

Borgatti, S. P., Mehra, A., Brass, D. J., and Labianca, G. (2009). Networkanalysis in the social sciences. Science, 323(5916):892–895.

Burnham, K. P. and Anderson, D. R. (2003). Model selection and multimodelinference: a practical information-theoretic approach. Springer Science & Busi-ness Media.

Carley, K. M., Pfeffer, J., Morstatter, F., and Liu, H. (2014). Embassiesburning: toward a near-real-time assessment of social media using geo-temporal dynamic network analytics. Social Network Analysis and Mining,4(1):195.

Dawson, S. (2010). ‘seeing’ the learning community: An exploration of thedevelopment of a resource for monitoring online student networking.British journal of educational technology: journal of the Council for EducationalTechnology, 41(5):736–752.

Gloor, P., Laubacher, R., Zhao, Y., and Dynes, S. (2004). Temporal visualiza-tion and analysis of social networks. In NAACSOS Conference, June, pages27–29.

Jiang, F., Wang, J., Hindle, A., and Nascimento, M. A. (2013). Mining thetemporal evolution of the android bug reporting community via slidingwindows. CoRR, abs/1310.7.

Kennedy, M. (2016). Open annotation and close reading the victorian text:Using hypothes.is with students. Journal of Victorian Culture, 0(0):1–9.

Kolaczyk, E. D. and Csárdi, G. (2014). Statistical Analysis of Network Data withR:. Use R! Springer New York.

ciii

civ Bibliography

Kraut, R., Olson, J., Banaji, M., Bruckman, A., Cohen, J., and Couper, M.(2004). Psychological research online: report of board of scientific affairs’advisory group on the conduct of research on the internet. The Americanpsychologist, 59(2):105–117.

Myllari, J., Ahlberg, M., and Dillon, P. (2010). The dynamics of an onlineknowledge building community: A 5-year longitudinal study. British jour-nal of educational technology: journal of the Council for Educational Technology,41(3):365–387.

Niglas, K. (2010). The multidimensional model of research methodology:An integrated set of continua. In Tashakkori, A. and Teddlie, C., editors,SAGE Handbook of Mixed Methods in Social & Behavioral Research, pages 215–236. SAGE, Thousand Oaks.

Raghavan, V., Steeg, G. V., Galstyan, A., and Tartakovsky, A. G. (2014). Mod-eling temporal activity patterns in dynamic social networks. IEEE Trans-actions on Computational Social Systems, 1(1):89–107.

Rivers, C. M. and Lewis, B. L. (2014). Ethical research standards in a worldof big data. F1000Research, 3.

Rodriguez, M. G., Leskovec, J., Balduzzi, D., and Schölkopf, B. (2014). Uncov-ering the structure and temporal dynamics of information propagation.Network Science, 2(1):26–65.

Scott, J. (2012). Social Network Analysis. SAGE.

Snijders, T. A. B. (2011). Statistical models for social networks. Annual reviewof sociology, 37(1):131–153.

Wickham, H. (2014). Tidy data. Journal of statistical software, 59(1):1–23.

Zhao, Y. and Weko, C. (2016). Network inference from grouped data.