Social Network Analysis case study

What is social network analysis (SNA)?

SNA is a method/process for studying the relationships between actors which include people, groups, organizations and any other information processing network members. Through SNA, we can extract the connection information between different nodes in order to figure out how can we make best use of social network to create value.

 

1.  Undirected case

For the given social network, we could easily make out various features for analysis consideration. This social network formed by 5 student with Degree Centrality given (L = 6, g = 5) .The Density of this social network is 2L/g(g-1) = 0.6.

 

 

Network Matrix

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

Centrality analysis

Group Degree Centralization:

    

If the geodesic distances are given, we could further analyze the ‘Closeness’ and ‘Betweenness’ properties.

2.   Directed case

There is no doubt we can easily find out David is the key player in this network on the 
undirected basis. But how about directed case?

  

Centrality analysis:

From the outgoing perspective, David is the most influential actor. The Degree Centrality of each student is illustrated below

	C'D
Alice	0.25
Bob	0.25
Carol	0.25
David	1
Eva	0.25

Prestige analysis:

On the other hand, the Degree Prestige considers the incoming direction and obviously Alice is the most prestigious actor in this social network.

Degree Prestige

	P'D
Alice	0.75
Bob	0.25
Carol	0.5
David	0.25
Eva	0.25

Distance Matrix

	Alice	Bob	Carol	David	Eva
Alice	0	0	1	0	0
Bob	1	0	2	0	0
Carol	1	0	0	0	0
David	1	1	1	0	1
Eva	2	2	2	1	0

Based on the distance relationship table, we can calculate the Proximity Prestige which considers how close all actors are to the particular actors. Standardized Proximity Prestige equation is

Proximity Prestige table

	Pp
Alice	0.8
Bob	0.33
Carol	0.67
David	0.25
Eva	0.25

The proximity has the same properties as the actor closeness centrality index. When all actors are adjacent to point i, its proximity prestige should be 1. While if point i is isolated, the result should equal to 0. Here Alice own the highest proximity prestige, so she is the most prestige person in this social network.