# Modularity Density Centrality

#### Definition

The modularity density centrality (C

^{K}) defined to be equal to the magnitudes of the elements of the first leading eigenvector belonging to the largest eigenvalue. That is, let λ = max(λ_{i}), i = 1, 2, · · · ,N. The vector v is the eigenvector belonging to λ, and the modularity density centrality score of node i, is the magnitude of the ith elements of vector v, i.e., |v_{i}|.#### Requirements

#### Software

#### References

- FU, L., GAO, L. & MA, X. 2010. A centrality measure based on spectral optimization of modularity density. Science China Information Sciences, 53, 1727-1737. DOI: 10.1007/s11432-010-4043-4