Consider this graph and answer the following questions If th

Solution

a) Identify the most active insurgent based on its “degree of centrality” and explain why it is so. ?

Solution) Degree centrality refers to the number of ties a node has to other nodes. Actors who have more ties may have multiple alternative ways and resources to reach goals—and thus be relatively advantaged.

from above network Degree of Centrality of each node are :-

Degree centrality of a node refers to the number of edges attached to the node.

In order to know the standardized score, you need to divide each score by n-1 (n = the number of nodes). Since the graph has 8 nodes, 7 (8-1) is the denominator for this question.

B - 2/7

D - 2/7

E - 2/7

F - 2/7

G - 2/7

M - 4/7

S - 2/7

Y - 2/7

Therefore the most active insurgent based on its “degree of centrality” is node \" M \"

b) Using the concept of “betweenness centrality” identify the single point of failure of this network.

Solution:>>Betweenness centrality measures the extent to which a vertex lies on paths between other vertices. Vertices with high betweenness may have considerable influence within a network by virtue of their control over information passing between others. They are also the ones whose removal from the network will most disrupt communications between other vertices because they lie on the largest number of paths taken by messages.

The betweenness centrality C_b(n) of a node n is computed as follows:
C_b(n) = _snt (_st (n) / _st),

From above Problem :

CM(M) = ((_gd(M) / _gd) + (_fd(M) / _fd) + (_bd(M) / _bd) + (_sd(M) / _sd) + (_se(M) / _se) + (_be(b) / _be) + (_ge(b) / _ge)+(_fe(b) / _fe)+(_gy(M) / _gy) +(_fy(M) / _fy)+(_by(M) / _by)+(_sy(M) / _sy) ) / 9

C_M(M)=(1/2 + 1/1 + 1/2 + 1/1 + 2/3 + 2/3 + 2/2 + 2/2 + 1/2 + 1/2 + 1/1)/9

C_M(M) = 0.925

Therefore the single point of failure of this network is M of  C_M(M) = 0.925.

C) If the network has been fragmented in a “left” subnetwork and a “right” subnetwork, what are the “high value targets” of the “left” subnetwork. Explain your answer.

SOLUTION:>> The left sub tree contains M, G, F , B ,S as Nodes.

NODE F and S are High valued Targets. Because of Degree Centrality of these nodes are:

Degree Centrality of NODE F = 3/4

     Degree Centrality of  NODE S = 3/4

     Degree Centrality of  NODE B= 2/4

      Degree Centrality of  NODE G= 2/4

     Degree Centrality of  NODE M= 324

Therefore by above Degree of Centrality Node F and Node S are HIGH VALUED TARGETS.