Social Networking Analysis of the Example

       This example network is  a 2-clique and 4-plex; and {A, B, D} and {A, C, D} form cliques. In this case, all nodes can reached by all other, so they have the same influence range 4; David is the cut-point which, if deleted, will make the network disconnected; and DE tie is the bridge which, if deleted, will also make the network disconnected. The example and the degree and degree centrality of each node are represented as follows:

	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	-

    So I think that David is the most important one in the network. To confirm and demonstrate my inference, I do some calculation of this example as follows.

       

        The density of this network is 0.6; group level degree centrality is 0.5; and group degree centralization is 2/3. We can get the geodesic distances as follow matrix.

	Alice	Bob	Carol	David	Eva
Alice	-	1	1	1	2
Bob	1	-	2	1	2
Carol	1	2	-	1	2
David	1	1	1	-	1
Eva	2	2	2	1	-

       Then we could calculate the degree, betweenness centrality, closeness centrality, degree centrality, degree prestige and proximity prestige of each member and group betweenness centralization, group closeness centralization and group degree centralization as follow. 

	Alice	Bob	Carol	David	Eva	Group
d	3	2	2	4	1	-
Cb’	1/12	0	0	7/12	0	9/16
Cc’	4/5	2/3	2/3	1	4/7	34/45
Cd’	3/4	1/2	1/2	1	1/4	2/3
Pd’	3/4	1/2	1/2	1	1/4	-
Pp	4/5	2/3	2/3	1	4/7	-

      The matrix could indicate that David is the most prestigious and influential as he has the largest value of each attribute; and his all attribute value are larger than the group centralized attribute.

       David with high degree values would send and receive many messages to others with a greater degree of influence and greater popularity or prestige within the network. Eva with low in-degree value indicates that she sends and receives few messages from the remaining students.So she  tends to be socially inactive and socially isolated from the rest of the class.

       In this network, D is more adaptive prefer to operate with more structure and with more of that structure consensually agreed; and E is more innovative prefer to operate using less structure and are less concerned with achieving consensus around the structure she uses. and substantial network connectivity are exhibited by A and D.

       After finishing my work, I have found that, despite different results from analyzing the same social network with different methods, they are representing the same thing in different ways. Different analyzing methods just describe different properties, and some methods can achieve the same result like degree centrality and degree prestige, closeness centrality and proximity prestige in this case.