Spectral Density of Complex Networks with a Finite Mean Degree

Details Spectral Density of Complex Networks with a Finite Mean Degree Spectral Density of Complex Networks with a Finite Mean Degree

2008-03-07

arxiv.org/abs/0803.1042v2

Physics

Condensed Matter

Statistical Mechanics

18 pages, 1 figure, minor corrections made

Scientific paper

10.1088/1751-8113/41/26/265002

In order to clarify the statistical features of complex networks, the spectral density of adjacency matrices has often been investigated. Adopting a static model introduced by Goh, Kahng and Kim, we analyse the spectral density of complex scale free networks. For that purpose, we utilize the replica method and effective medium approximation (EMA) in statistical mechanics. As a result, we identify a new integral equation which determines the asymptotic spectral density of scale free networks with a finite mean degree $p$. In the limit $p \to \infty$, known asymptotic formulae are rederived. Moreover, the $1/p$ corrections to known results are analytically calculated by a perturbative method.

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