In this paper, we argue that only sufficient increase in distance between the nodes which can virtually disconnect the graph is necessary instead of the physical disconnection of the network to identify the key players in a network. A procedure is described for finding sets of key players in a social network. A key assumption is that the importance of a node v not only depends on the cohesion of its personal network but also depends on, to which extent the immediate neighbors and indirect contacts of node v are connected with each other. Therefore, a new measure of importance of a node in a network has been described which suggests the best node whose removal maximally increases the distances between rests of the nodes to virtually disconnect the graph at-least. Moreover, an algorithm based on network disruption has also been described which uses the proposed measure and chooses a single or group of nodes as key players in a network.
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