A centrality measure based on spectral optimization of modularity density

Centrality analysis has been shown to be a valuable method for the structural analysis of complex networks.It is used to identify key elements within networks and to rank network elements such that experiments can be tailored to interesting candidates.In this paper,we show that the optimization process of modularity density can be written in terms of the eigenspectrum of kernel matrix.Based on the eigenvectors belonging to the largest eigenvalue of kernel matrix,we present a new centrality measure that characterizes the contribution of each node to its assigned community in a network,called modularity density centrality.The measure is illustrated and compared with the standard centrality measures by using respectively an artificial example and a classic network data set.The statistical distribution of modularity density centrality is investigated by considering large computer generated graphs and two large networks from the real world.Experimental results show the significance of the proposed approach.