# Modularity Centrality

#### Definition

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 non-overlapping 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**#### Requirements

#### Software

#### References

- 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