Modularity Centrality


The modularity centrality (CM) 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 non-overlapping community numbers, βj is jth eigenvalue of the modularity matrix, uj is eigenvector corresponding to βj , and xk is kth row vector of assignment matrix. Let β = max(|βj|), if ui is the magnitude of the ith elements of eigenvector uj corresponding to β. Then the modularity centrality of node i is defined as:

See Modularity Density Centrality




  • WANG, G., SHEN, Y. & LUAN, E. 2008. A measure of centrality based on modularity matrix. Progress in Natural Science, 18, 1043-1047. DOI: 10.1016/j.pnsc.2008.03.015 Publisher web site Endnote RIS file


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