Spectral densities of scale-free networks

TL;DR

This paper analyzes the spectral densities of various matrices associated with scale-free networks using the replica method, providing explicit results for large networks with arbitrary degree exponents and weight parameters.

Contribution

It introduces a novel analytical approach to compute spectral densities of weighted matrices in scale-free networks, extending understanding of their spectral properties.

Findings

Explicit spectral density formulas for large scale-free networks.

Results valid for arbitrary degree exponents and weight parameters.

Enhanced understanding of spectral properties in complex networks.

Abstract

The spectral densities of the weighted Laplacian, random walk and weighted adjacency matrices associated with a random complex network are studied using the replica method. The link weights are parametrized by a weight exponent $\beta$. Explicit results are obtained for scale-free networks in the limit of large mean degree after the thermodynamic limit, for arbitrary degree exponent and $\beta$.