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Community CentralityDefinition
(I)
[NEWMAN, M. E. J. 2006] (II) For node i the community centrality is: where the main sum is over the N communities to which node i belongs, and S(j,k) refers to the similarity between community j and k, calculated as the Jaccard coefficient for the number of shared nodes between each community pair, and this is averaged over the m communities paired with community j and in which node i jointly belongs. [KALINKA, A. T. 2011] (III) Community centrality of a given edge (or node) was defined as the sum of local influence zones of all network edges (or nodes) including the given edge. Thus community centrality represents an integrated measure of the whole network’s influence to one of its edges or nodes. It is worth to note that the community centrality measure we use is not the same community centrality measure introduced by Mark Newman [2006]. The two community centralities are similar in the sense that they take into account the mesoscopic (modular) structure of the network to define the centrality value. However, the Newmantype community centrality is derived from eigenvector analysis, while ours represents the sum of local influence zones of all nodes or edges on each node or edge. [SZALAYBEKŐ, M., 2012] SoftwareReferences
