EIWCS: Characterizing Edges Importance to Weaken Community Structure

Edges in a network can be divided into two kinds according to their different roles when removed from the network: some enhance the community structure like the ones connecting two communities while others contribute to weaken the community structure like the ones inside a community. In this paper, we define the edge important to weaken community structure as the relative change in the eigenvalues of the network adjacency matrix upon their removal, which is called EIWCS. Experimental results on real-world network and artificial networks indicate the EIWCS index can well characterize edges important to weaken community structure.