Entropic Dynamics of Networks

TL;DR

This paper introduces an entropic dynamics framework for networks based on maximum entropy principles, deriving a diffusion process for graph evolution and comparing it to real-world network degree distributions.

Contribution

It develops a novel entropic dynamics formalism for networks using information geometry, providing a new way to model network evolution.

Findings

The dynamics are described by a diffusion equation derived from maximum entropy principles.

The steady state of the dynamics aligns with degree distributions observed in real networks.

The framework applies to Gibbs distributions with node connectivity constraints.

Abstract

Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into account the natural information geometry of probability distributions. We apply this framework to the Gibbs distribution of random graphs obtained with constraints on the node connectivity. The information geometry for this graph ensemble is calculated and the dynamical process is obtained as a diffusion equation. We compare the steady state of this dynamics to degree distributions found on real-world networks.