Riemannian-geometric entropy for measuring network complexity

TL;DR

This paper introduces a novel Riemannian geometric entropy measure for networks, effectively quantifying their complexity and detecting phase transitions across various network models and real-world data.

Contribution

It proposes a new entropy based on information geometry that can be applied to any network to measure its complexity and identify phase transitions.

Findings

Successfully detects phase transitions in random and scale-free networks

Effectively characterizes small exponential random graphs and configuration models

Applies to real-world networks to measure complexity

Abstract

A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a - in principle any - network a differentiable object (a Riemannian manifold) whose volume is used to define an entropy. The effectiveness of the latter to measure networks complexity is successfully proved through its capability of detecting a classical phase transition occurring in both random graphs and scale--free networks, as well as of characterizing small Exponential random graphs, Configuration Models and real networks.