A star based model for the eigenvalue power law of Internet graphs

TL;DR

This paper demonstrates that the eigenvalue power law observed in Internet graphs arises from their degree distribution and the prevalence of star subgraphs, using a simple deterministic model.

Contribution

It introduces a deterministic model linking eigenvalue distribution to degree distribution and star subgraphs in Internet graphs.

Findings

Eigenvalue power law is a consequence of degree distribution.

Internet graphs contain many star subgraphs.

Model explains spectral properties of Internet graphs.

Abstract

Using a simple deterministic model for the Internet graph we show that the eigenvalue power law distribution for its adjacency matrix is a direct consequence of the degree distribution and that the graph must contain many star subgraphs.