Social Networking 3: Case Study of Social Network Analysis

 What is social network analysis (SNA)?

Social Network Analysis is the study of the pattern of interaction between actors. Participants in the community are called actors such as people, groups, organizations and other information/knowledge entities. In SNA actors are depicted nodes, and valued relations between actors are depicted as links, or ties, either directed or undirected, between the corresponding nodes. SNA focuses on the social actor and relationship between the actors.

Describe the above social network according to the knowledge that I have learned in lecture 6-8.

For Alice, she has relationships with Bob, David and Carol.

For Bob, he has relationships with Alice and David.

For Carol, she has relationships with Alice and David.

For David, he has relationships with all the other 4 actors: Alice, Bob, Carol and Eva.

For Eva, she only has a relationship with David.

To present clearly, I denote their relationships by following social-matrix.

	Alice	Bob	Carol	David	Eva
Alice	-	1	1	1	0
Bob	1	-	0	1	0
Carol	1	0	-	1	0
David	1	1	1	-	1
Eva	0	0	0	1	-

As can be seen, it is a symmetric matrix along the diagonal. That is because I consider it to be a unidirectional network just like the pattern in Facebook.

This diagram comprises of 5 nodes and 6 ties (i.e. g = 5, L = 6). Then the Density is 2L/g(g-1) = 0.6.

The Group Degree Centralization:

Within this social network, who is the most influential?

Usually the most influential participant is also the most important one. In order to measure the importance of each node, we have three standard centrality measures capture a wide range of “importance” in a network: (1) Degree Centrality (2) Closeness Centrality (3) Between-ness Centrality.

Firstly, let’s calculate the degree centrality. It can be normalized as C’_D = d(n_i)/(g-1). Below is the degree centrality table.

	Degree Centrality
Alice	0.75
Bob	0.5
Carol	0.5
David	1
Eva	0.25

Degree centrality is the sum of all other actors who are directly connected to the actor in concern. It signifies activity or popularity. Through above table, David has the largest value of Degree Centrality which means David is the most popular one.

Secondly, we study it in terms of Closeness Centrality. Closeness represents the mean of the geodesic distances between some particular node and all other nodes connected with in. An actor is considered important if he/she is relatively close to all other actors. The normalized closeness centrality is as following.

	C’c (ni)
Alice	0.8
Bob	0.68
Carol	0.68
David	1
Eva	0.56

This parameter shows that David has the largest closeness. He is the most influential one for he is close to everyone.

Last but not least, we evaluate the Between-ness Centrality. It is a measure of the potential for control as an actor who is high in “between-ness” is able to act as a gatekeeper controlling the flow of resources between the alters that he or she connects.

According to the formula, we have C_B(Alice) = 0.5, C_B(Bob) = 0, C_B(Carol) = 0, C_B(David) = 3.5, C_B(Eva) = 0. Then the normalized results are as following.

	C’B (ni)
Alice	0.08
Bob	0
Carol	0
David	0.58
Eva	0

David has the biggest power as a gatekeeper.

Therefore, David is the most influential actor in this social network.

Suppose you are conducting a research on the social network of these five students and the above results are obtained, discuss the finding s and their implications based on your data.

My finding is that “Winners take all” is very common in a social network. The most active and popular actor usually is also the closest participant to the other partner. And he plays an important role in keeping this social network inter-connected.