Spectral properties of adjacency and distance matrices for various networks

TL;DR

This paper analyzes the spectral characteristics of adjacency and distance matrices across different network models, providing analytical results for dense Erdos-Renyi graphs and comparing spectral properties among exponential, scale-free, and classical random networks.

Contribution

It offers a comparative spectral analysis of various network types and derives analytical spectra for dense Erdos-Renyi graphs, advancing understanding of network spectra.

Findings

Spectral properties vary significantly across network types.

Analytical spectra derived for dense Erdos-Renyi graphs.

Comparison highlights differences in spectral distributions.

Abstract

The spectral properties of the adjacency (connectivity) and distance matrix for various types of networks: exponential, scale-free (Albert--Barabasi) and classical random ones (Erdos--Renyi) are evaluated. The graph spectra for dense graph in the Erdos-Renyi model are derived analytically.