Social Network Analysis

• Tools for SNA • Page Rank Algorithm • Hierarchical Clustering • Recommendation System based on SNA (Collaborative Filtering) • How Facebook/Amazon uses SNA for recommendations? • Two Hop degree • Dynamism in Friendship Network of CSE-B • Online Social Networks and Clusters • Influential Nodes and Their Importance • Bibliography • Question - Answer Session

By Sohom Ghosh

TOPICS:

Tools for Analyzing Social Networks

• Gephi

• Pajek

• NetworkX (Python package)

• iGraph (Python and R package)

Gephi

Pajek

NetworkX

• iGraph is similar.

• >>> import networkx as nx

• >>> G=nx.Graph()

• >>> G.add_edge(1,2) # default edge data=1

• >>> G.add_edge(2,3,weight=0.9) # specify edge data

• >>> print(nx.dijkstra_path(G,'a','d'))

Page Rank Algorithm

• PageRank works by counting the number and quality of links to a page to determine a rough estimate of how important the website is. The underlying assumption is that more important websites are likely to receive more links from other websites

• The original PageRank algorithm was described by Lawrence Page and Sergey Brin

in several publications. It is given by

where PR(A) is the PageRank of page A, PR(Ti) is the PageRank of pages Ti which link to page A, C(Ti) is the number of outbound links on page Ti and d is a damping factor which can be set between 0 and 1.

PR(A) = (1-d) + d (PR(T1)/C(T1) + ... + PR(Tn)/C(Tn))

Hierarchical Clustering

• Process:-

1. After calculating “distances”, “weights” between all pairs of vertices

2. Start with all n nodes treating them as disconnected

3. Add edges between pairs one by

one in order of decreasing weights

RESULT: Nested components, where one

can take a ‘slice’ at any level of the tree.

Dendogram

Data Point

Dis

tan

ce

Recommendation System Based on SNA (Collaborative Filtering)

• Collaborative Filtering is a method of making automatic predictions

about the interests of a user by collecting preferences or taste

information from many users from a perspective of collaboration. The

underlying assumption of this approach is that, if a person A has the

same opinion as that of person B on an issue, then A is more likely to

follow B’s opinion on a different issue x than to follow the opinion of a

person chosen randomly.

Ex:- Samujjal and Sayantan have 83 mutual friends in common and are

room mates. If Sayantan buys a moto E smartphone, Samujjal is most likely

to buy it in future. In this case we should recommend him this phone.

How Facebook/LinkedIn analyses Social Networks for Recommendations?

Analysis

• Mutual Friends

• Friend Circle and Network

• Interactions

• Liked Pages/Interests

• Age Group

Two Hop Degree

• Two hop degree of an item represents a node’s ability to extend its

reach beyond its immediate neighbors. Its significance lies in the

realization of influence that a node exerts on its neighbors. A node

with higher amount of two hop degree distribution form the core

part of that group.

• If two nodes are not adjacent and have at least one mutual friend,

then they are at a distance of Two Hop from each other. Our friends

of friends are at a distance two hop from us.

• E.g. “BLUE EYES” :P

Dynamism in Friendship Network of CSE-B

1

2

4

3

6

5

Protim

Arijit

Sayantan

Pramit

Rajpratim

Utsab

1st Year

7

SnG

Dynamism in Friendship Network of CSE-B

1

2

4

3

6

5

Protim

Arijit

Sayantan

Pramit

Rajpratim

Utsab

2nd Year 1st Sem

7

SnG

8 RS

9

Samujjal

1

2

4

3

6 Arijit

Sayantan

Pramit

Rajpratim

Utsab

2nd Year 2nd Sem

7

SnG

8

RS

9

Samujjal

1

2

4

3

6 Arijit

Sayantan

Pramit

Rajpratim

Utsab

3rd Year 1st Sem

7

SnG

8

RS

9

Samujjal

1

2

4

3

6 Arijit

Sayantan

Pramit

Rajpratim

Utsab

3rd Year 2nd Sem (Expected)

7

SnG

8

RS

9

Samujjal

Dynamism in Friendship Network of CSE-B

Quiz

• Who is RS and SnG???

Online Social Networks and Clusters

Online Social Networks and Clusters

Influential Nodes and Their Importance

• “More Connected”

• “Degree”, “Betweenness” , “Closeness” more

• “Teachers” in villages.

• For “CLEAN INDIA” drive, famous Bollywood actors and celebrities

are nominated as campaigner. This is because they have lots of fans

and are influential nodes in the network.

Bibliography

• http://www.slideshare.net/gcheliotis/social-network-analysis-

3273045

• www.images.google.com

• https://www.coursera.org/course/sna

• Presentation by James Moody on Social Network Analysis at

American Sociological Association, San Francisco, August 2004

• Data Mining for Social Network Analysis, IEEE ICDM 2006, Hong

Kong, Jaideep Srivastava, Nishith Pathak, Sandeep Mane,

Muhammas A. Ahamad University of Minnesota

Questions and Answers