Social Network Analysis

1. Describe briefly what is social network analysis(SNA)

A social network is a group of collaborating individuals or entities that are related to each other.

SNA(Social Network Analysis) is the study of the pattern of interaction between actors which focuses on the social actor and the relationship between the actors.

In SNA, Social network is formally defined as a set of social actors, or nodes, members that are connected by one or more types of relations. The units are most commonly individuals, groups or organizations, but in principle any units that can be connected to other units can be studied as nodes, such as web pages, blogs, emails, instant messages, families, journal articles, neighborhoods, classes, sectors within organizations, positions, or nations.

2. Example to explain the social network analysis

The following is a social network formed by 5 students.

(a). Describe the above social network according to your best knowledge.

It seems to be one mode network since the five people are of the same type. And this graph is a undirected graph. It consists a set of nodes and links. And the direction of a link is not presented, in which case the existence of a link between Alice and David necessarily implies the existence of a link from David to Alice.

I think acquaintances or friends can be the relation between them.

Alice knows Bob, Carol and David.

Bob knows Alice and David.

Carol knows Alice and David.

David knows Alice, Bob, Carol and Eva.

Eva only knows David.

The two people linked with each other know each other or they are friends or acquaintances.

Of course, the network or links can be some other kinds of relations which are undirected in social network.

(b). Within this social network, who is the most influential?

1). Present the network in a 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	-

It seems that David have the most connection in this network.

2). Density:

Density of the network:

3). Centrality

Centrality identify which nodes are in the ‘center’ of the network.

Degree Centrality: Degree centrality is the sum of all other actors who are directly connected to the actor in concern.

According to the definition:

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

Closeness Centrality: Closeness represents the mean of the geodesic distances between some particular node and all other nodes connected with in. Describes the average distances between one node and all other nodes connected with it.

According to the definition:

	Closeness Centrality
Alice	0.8
Bob	0.67
Carol	0.67
David	1
Eva	0.57

Betweenness Centrality: It is a measure of the potential for control as an actor who is high in “betweenness” is able to act as a gatekeeper controlling the flow of resources (information, money, power, e.g.) between the alters that he or she connects.

According to the definition:

	Betweenness Centrality
Alice	0.17
Bob	0
Carol	0
David	0.83
Eva	0

After the comparison, we can find that the value for David whether it is in the degree centrality, closeness centrality or betweenness centrality is bigger than the other four people. David has the most connections with the other four people. If you want to transmit some information in this network, the best way is to transmit the information through David in most case. Besides, David functions as a gatekeeper who can control the flow of information etc in this network. If you want to control this network, the best way is to control David.

(c). Findings and implications based on the data.

Except the information that David is the key node in this network, we can find Eva is almost an isolate node except the connection with David. Information etc can be transmitted without passing through Bob, Carol and Eva. Bob and Carol seem to be not so important in this network except Eva.

If this is a relationship network, we can find that David and Alice might be more outgoing and easygoing. They have more friends and they can get more information. David might be the head of the group. Eva might be shy who will not make friends with strangers easily.

If this is a social network on the Internet, twitter for instance, we can guess the information on David’s or Alice’s homepage must be more interesting than the others. They have higher reputation than the others. And they must log on the website frequently. Eva might just simply register on the website and forget about it after that. David and Alice is more active in this social network. And you can get more information about all the five people and even make friends with them through David if you also have connection with David. This is the fastest way to get into this network.