Social Network Analysis (SNA) is the study of the pattern of interaction between actors and focuses on the social actor and the relationship between the actors. Social network analysis refers to methods used to analyze social networks, social structures made up of individuals (or organizations) called "nodes", which are tied (connected) by one or more specific types of interdependency, such as web pages, blogs, emails, instant messages, families, journal articles, neighborhoods, classes, sectors within organizations, positions, or nations. Nodes, or network members, are the units that are connected by the relations whose patterns researchers study. 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.
The graphical representation (Sociograph) of social network above has five nodes; they are Alice, Bob, Carol, David and Eva. The links (ties) between these five nodes are undirected.Itis one mode networks. This networks can be represented by a simple 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
|
–
|
The cutpoint of this networks is node “David”, because if David is deleted, it will make the network disconnected.
The degree of every node is below:
d(nAlice)=3
d(nBob)=2
d(nCarol)=2
d(nDavid)=4
d(nEva)=1
For this undirectional graph, density is
=L/g(g-1)/2=6/5(5-1)/2=0.6
= = =0.6
The geodesic distances between every two nodes are …
d(Alice, Bob)=1
d(Alice, Carol)=1
d(Alice, David)=1
d(Alice, Eva)=2
d(Bob, Carol)=2
d(Bob, David)=1
d(Bob, Eva)=2
d(Carol, David)=1
d(Carol, Eva)=2
d(David, Eva)=1
{Alice, Carol, David} and {Alice, Bob, David} are cliques.
{Alice, Bob, Carol, David, Eva} is a 2-clique.
{Alice, Bob, Carol, David} is a 2-plex.
Within this social network, David is the most influential. Three standard centrality measures will help us to find the most influential; they are degree centrality, closeness centrality and betweenness centrality. Centrality identify which nodes are in the ‘center’ of the network and the “key player”. In a social network, nodes at the center can be very important
Firstly, Degree centrality of this network shows as below. The degree centrality of node “David” is 4, the highest in these five nodes.
Secondly, the closeness centrality below shows the actor “David” is considered the most important, because it is relatively close to all other actors.
(4-1)+(4-2)+(4-2)+(4-3)/4*3=0.667
The group degree centralization is 0.667.
Group Degree Closeness Centralization
Closeness is based on the inverse of the geodesic distance of each actor to every other actor, therefore the shorter the distance is, the larger the closeness will be.
Alice:0.8
Bob:0.667
Carol:0.667
David:1
Eva:0.57
By using this formula, the group closeness can be calculated out as 0.756.
Group Betweenness Centralization
Alice=1/12
Bob=Carol=Eva=0
David=7/12
In this social network, the group betweeness centralization is 0.5625.
Therefore,Through the above algorithms results, we can image that “David” is considered the most important on the social network of these five students .
