Upload
julia-newman
View
227
Download
0
Tags:
Embed Size (px)
Citation preview
How to Analyse Social Network?
Social networks can be represented by complex networks.
Reviews
Social network is a social structure made up of individuals (or organizations) called “nodes”, which are connected by one or more types of relationships, represented by “links”. Friendship Kinship Common Interest ….
Graph-based structures are very complex.
2
Source: http://followingfactory.com/
Introduction
Various nature and society systems can be described as complex networks social systems, biological systems, and communication systems.
3
By presented as a graph, vertices (nodes) represent individuals or organizations and edges (links) represent interaction among them
Source: http://www.fmsasg.com/SocialNetworkAnalysis
Types of Network Models
The network of co-authorship relationships in SEG's journal Geophysics is scale-free
4
Source: http://www.agilegeoscience.com/journal/tag/networks
Degree: The degree of a vertex counts the number of
edges that
Oriented Degree when Edges Directed: The in-degree of a vertex (deg-) counts the
number of edges that stick in to the vertex. The out-degree (deg+) counts the number
sticking out.
5
Network Analysis
There are various measures of the centrality of a vertex within a graph that determine the relative importance of a vertex within the graph how important a person is within a social network
who is the most well-known author in the citation network
6
Centrality Measures
Degree centrality Degree centrality is defined as the number of links incident upon
a node (i.e., the number of ties that a node has).
Degree is often interpreted in terms of the immediate risk of node
for catching whatever is flowing through the network such as a virus, or some information.
If the network is directed (meaning that ties have direction), then we usually define two separate measures of degree centrality, namely indegree and outdegree.
7
Centrality Measures
Degree centrality Indegree is a count of the number of ties directed to
the node. Outdegree is the number of ties that the node directs
to others. For positive relations such as friendship or advice, we
normally interpret indegree as a form of popularity, and outdegree as gregariousness.
8
Centrality Measures
Degree centrality An entity with high degree centrality:
Is generally an active player in the network. Is often a connector or hub in the network. Is not necessarily the most connected entity in the network
(an entity may have a large number of relationships, the majority of which point to low-level entities).
May be in an advantaged position in the network. May have alternative avenues to satisfy organizational
needs, and consequently may be less dependent on other individuals.
Can often be identified as third parties or deal makers.
9
Centrality Measures
Degree centrality An entity with high degree centrality:
Alice has the highest degree centrality, which means that she is quite active in the network. However, she is not necessarily the most powerful person because she is only directly connected within one degree to people in her clique—she has to go through Rafael to get to other cliques.
10
Centrality Measures
Source: http://www.fmsasg.com/SocialNetworkAnalysis/
Degree centrality
11
Centrality Measures
Betweenness Centrality Betweenness is a centrality measure of a vertex within
a graph. Vertices that occur on many shortest paths between
other vertices have higher betweenness than those that do not.
12
Centrality Measures
Betweenness Centrality An entity with a high betweenness centrality
generally: Holds a favored or powerful position in the network. Represents a single point of failure—take the single
betweenness spanner out of a network and you sever ties between cliques.
Has a greater amount of influence over what happens in a network.
13
Centrality Measures
Betweenness Centrality An entity with a high betweenness centrality
generally:
Rafael has the highest betweenness because he is between Alice and Aldo, who are between other entities. Alice and Aldo have a slightly lower betweenness because they are essentially only between their own cliques. Therefore, although Alice has a higher degree centrality, Rafael has more importance in the network in certain respects.
14
Centrality Measures
Source: http://www.fmsasg.com/SocialNetworkAnalysis/
Betweenness centrality
15
Centrality Measures
Closeness Centrality Closeness is one of the basic concepts in a topological
space. We say two sets are close if they are arbitrarily near to each
other. The concept can be defined naturally in a metric space where a
notion of distance between elements of the space is defined, but it can be generalized to topological spaces where we have no concrete way to measure distances.
16
Centrality Measures
Closeness Centrality Closeness is a centrality measure of a vertex within a graph.
Vertices that are 'shallow' to other vertices (that is, those that tend to have short geodesic distances to other vertices with in the graph) have higher closeness.
Closeness is preferred in network analysis to mean shortest-path length, as it gives higher values to more central vertices, and so is usually positively associated with other measures such as degree.
Closeness centrality measures how quickly an entity can access more entities in a network
17
Centrality Measures
Closeness Centrality An entity with a high closeness centrality
generally: Has quick access to other entities in a network. Has a short path to other entities. Is close to other entities. Has high visibility as to what is happening in the
network.
18
Centrality Measures
Closeness Centrality
Rafael has the highest closeness centrality because he can reach more entities through shorter paths. As such, Rafael's placement allows him to connect to entities in his own clique, and to entities that span cliques.
19
Centrality Measures
Source: http://www.fmsasg.com/SocialNetworkAnalysis/
Hub and Authority (for directed graph) If an entity has a high number of relationships pointing to it, it has a high
authority value, and generally: Is a knowledge or organizational authority within a domain. Acts as definitive source of information.
Hubs are entities that point to a relatively large number of authorities. They are essentially the mutually reinforcing analogues to authorities. Authorities point to high hubs. Hubs point to high authorities. You cannot have one without the other.
20
Centrality Measures
Source: http://www.fmsasg.com/SocialNetworkAnalysis/
Eigenvector Centrality Eigenvector centrality is a measure of the
importance of a node in a network. It assigns relative scores to all nodes in the network based on the principle that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes.
Google's PageRank is a variant of the Eigenvector centrality measure.
21
Centrality Measures
Eigenvector Centrality
22
Centrality Measures
Eigenvector Centrality
23
Centrality Measures
24
Centrality Measures
25
RFID Datenvolumen Centrality Measures
PageRank
Only Structure Consideration
Knowledge of Global Network Structure
Broken Link Problems
KONECT: the Koblenz Network Collection contains 168 network datasets (for instance)
Animal networks are networks of contacts between animals. Authorship networks are unweighted bipartite networks
consisting of links between authors and their works. Citation networks consist of documents that reference each
other. Coauthorship networks are unipartite network connecting
authors who have written works together. Communication networks contain edges that represent
individual messages between persons. consists of Matlab code to generate statistics and plots
about them
26
Social Network Analysis Software
Source: konect.uni-koblenz.de/networks
“Pajek”: Large Network Analysis Software
2828
Introduction to Slovenian Spider: Pajek
http://vlado.fmf.uni-lj.si/pub/networks/pajek/ Free software Windows 32 bit
Pajek 2.05
“Whom would you choose as a friend ?”
2929
Introduction
Its applications: Communication networks: links among pages or
servers on Internet, usage of phone calls Transportation networks Flow graphs of programs Bibliographies, citation networks
30
Data Structures
Six data structures: Network(*.net) – main object (vertices and lines - arcs, edg
es) Partition(*.clu) – nominal property of vertices (gender); Vector(*.vec) – numerical property of vertices; permutation (*.per) – reordering of vertices; cluster (*.cls) – subset of vertices (e.g. a cluster from partiti
on); hierarchy (*.hie) – hierarchically ordered clusters and vertic
es.
31
Introduction
Pajek 2.05
32
Network Definitions
Graph Theory Graphs represent the structure of networks
Directed and undirected graphs Lists of vertices arcs and edges, where each arch
and edge has a value. To view the network data files: NotePad, EditPlus
33
Network Data File
33
Open Network Data File (*.net)
Number of Vertices
34
Transform
Transform
35
Report Information
36
Visualization
Energy – Idea: the network is represented like a physical system, and we are searching for the state with minimal energy. Two algorithms are included:
Layout/Energy/Kamada-Kawai – slower Layout/Energy/Fruchterman-Reingold – faster, drawing in a plane or space (2D or
3D), and selecting the repulsion factor
37
Network Creation
37
38
Partitions
File name: *.clu
39
Degree
Social Network Analysis: Theory and Applications
Graphs (ppt), Zeph Grunschlag, 2001-2002. KONECT:
http://konect.uni-koblenz.de/networks Pajek:
http://pajek.imfm.si/doku.php?id=download http://www.fmsasg.com/SocialNetworkAnalysis/
40
References