A statistical mechanics approach for scale-free networks and finite-scale networks

TL;DR

This paper introduces a statistical mechanics framework to analyze complex networks, deriving degree distributions that extremize free energy, and identifies conditions leading to scale-free and finite-scale networks, validated through simulations.

Contribution

It develops a novel statistical mechanics approach to characterize complex networks and derives conditions for scale-free and finite-scale degree distributions.

Findings

Identifies conditions for scale-free degree distributions.

Derives finite-scale degree distributions.

Validates theoretical results with network simulations.

Abstract

We present a statistical mechanics approach for the description of complex networks. We first define an energy and an entropy associated to a degree distribution which have a geometrical interpretation. Next we evaluate the distribution which extremize the free energy of the network. We find two important limiting cases: a scale-free degree distribution and a finite-scale degree distribution. The size of the space of allowed simple networks given these distribution is evaluated in the large network limit. Results are compared with simulations of algorithms generating these networks.