The entropy of randomized network ensembles

TL;DR

This paper investigates the entropy of various randomized network ensembles to understand their structural complexity and how specific features like degree distribution influence network order.

Contribution

It introduces entropy as a measure to quantify the structural information content of network ensembles with fixed features, providing new insights into network organization.

Findings

Scale-free networks have lower entropy than homogeneous networks.

Entropy can assess the importance of structural features in real networks.

Randomized ensembles with fixed degree distributions show varying levels of order.

Abstract

Randomized network ensembles are the null models of real networks and are extensivelly used to compare a real system to a null hypothesis. In this paper we study network ensembles with the same degree distribution, the same degree-correlations or the same community structure of any given real network. We characterize these randomized network ensembles by their entropy, i.e. the normalized logarithm of the total number of networks which are part of these ensembles. We estimate the entropy of randomized ensembles starting from a large set of real directed and undirected networks. We propose entropy as an indicator to assess the role of each structural feature in a given real network.We observe that the ensembles with fixed scale-free degree distribution have smaller entropy than the ensembles with homogeneous degree distribution indicating a higher level of order in scale-free networks.