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Modularity CentralityDefinition
The modularity centrality (C^{M}) is based on the idea that nodes are tied to their assigned communities
by the “strength” which shows the importance of nodes belonging to their communities, Q value is
expressed as
where p is nonoverlapping community numbers, β_{j} is jth eigenvalue of the modularity matrix, u_{j} is
eigenvector corresponding to β_{j} , and x_{k} is kth row vector of assignment matrix. Let β = max(β_{j}),
if u_{i} is the magnitude of the ith elements of eigenvector u_{j} corresponding to β. Then the modularity
centrality of node i is defined as:
See Modularity Density Centrality RequirementsSoftwareReferences
