Spectral Density of Complex Networks with Two Species of Nodes

Taro Nagao

Published 2012-08-25, updated 2013-01-07Version 2

The adjacency and Laplacian matrices of complex networks with two species of nodes are studied and the spectral density is evaluated by using the replica method in statistical physics. The network nodes are classified into two species (A and B) and the connections are made only between the nodes of different species. A static model of such bipartite networks with power law degree distributions is introduced by applying Goh, Kahng and Kim's method to construct scale free networks. As a result, the spectral density is shown to obey a power law in the limit of large mean degree.