Entropy measures for complex networks: Toward an information theory of complex topologies

TL;DR

This paper extends information theory concepts to complex networks by defining Shannon entropy for network ensembles, aiding in null model formulation and inference in complex network analysis.

Contribution

It introduces a method to define Shannon entropy for network ensembles and relates it to Gibbs and von Neumann entropies, advancing the theoretical framework of network complexity.

Findings

Defines Shannon entropy for network ensembles.

Relates network entropy to Gibbs and von Neumann entropies.

Facilitates null model creation and inference in network science.

Abstract

The quantification of the complexity of networks is, today, a fundamental problem in the physics of complex systems. A possible roadmap to solve the problem is via extending key concepts of information theory to networks. In this paper we propose how to define the Shannon entropy of a network ensemble and how it relates to the Gibbs and von Neumann entropies of network ensembles. The quantities we introduce here will play a crucial role for the formulation of null models of networks through maximum-entropy arguments and will contribute to inference problems emerging in the field of complex networks.