# Mapping and discrimination of networks in the complexity-entropy plane

## TL;DR

This paper introduces a statistical complexity measure based on entropy and disequilibrium to classify and analyze complex networks, effectively distinguishing different network types and optimizing threshold selection.

## Contribution

It applies a novel complexity-entropy framework to classify real-world and model networks, demonstrating its effectiveness in network discrimination and threshold optimization.

## Key findings

- Networks of the same category cluster in the complexity-entropy plane.
- Connectome networks show high complexity, while infrastructure networks show lower.
- The framework aids in objectively constructing threshold-based networks.

## Abstract

Complex networks are usually characterized in terms of their topological, spatial, or information-theoretic properties and combinations of the associated metrics are used to discriminate networks into different classes or categories. However, even with the present variety of characteristics at hand it still remains a subject of current research to appropriately quantify a network's complexity and correspondingly discriminate between different types of complex networks, like infrastructure or social networks, on such a basis. Here, we explore the possibility to classify complex networks by means of a statistical complexity measure that has formerly been successfully applied to distinguish different types of chaotic and stochastic time series. It is composed of a network's averaged per-node entropic measure characterizing the network's information content and the associated Jenson-Shannon divergence as a measure of disequilibrium. We study 29 real world networks and show that networks of the same category tend to cluster in distinct areas of the resulting complexity-entropy plane. We demonstrate that within our framework, connectome networks exhibit among the highest complexity while, e.g, transportation and infrastructure networks display significantly lower values. Furthermore, we demonstrate the utility of our framework by applying it to families of random scale-free and Watts-Strogatz model networks. We then show in a second application that the proposed framework is useful to objectively construct threshold-based networks, such as functional climate networks or recurrence networks, by choosing the threshold such that the statistical network complexity is maximized.