Spectral Density of Complex Networks with Two Species of Nodes

TL;DR

This paper analyzes the spectral density of bipartite complex networks with two node species, revealing a power-law behavior in the spectral density for large mean degrees using the replica method.

Contribution

It introduces a static bipartite network model with power law degree distributions and evaluates its spectral density analytically.

Findings

Spectral density follows a power law at large mean degrees.

Networks are bipartite with two node species and scale-free degree distributions.

Analytical results obtained via the replica method.

Abstract

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.