The Shannon and the Von Neumann entropy of random networks with heterogeneous expected degree

TL;DR

This paper explores the relationship between Shannon and Von Neumann entropies in networks with heterogeneous degree distributions, revealing a correlation that suggests a link between classical and quantum descriptions of network complexity.

Contribution

It demonstrates a correlation between Shannon and Von Neumann entropies in networks with heterogeneous degrees, highlighting a potential equivalence between classical and quantum network complexity measures.

Findings

Correlation between Shannon and Von Neumann entropies in heterogeneous networks

Heterogeneity in degree distribution influences entropy relationship

Suggests a link between classical and quantum network descriptions

Abstract

Entropic measures of complexity are able to quantify the information encoded in complex network structures. Several entropic measures have been proposed in this respect. Here we study the relation between the Shannon entropy and the Von Neumann entropy of networks with a given expected degree sequence. We find in different examples of network topologies that when the degree distribution contains some heterogeneity, an intriguing correlation emerges between the two entropies. This result seems to suggest that this kind of heterogeneity is implying an equivalence between a quantum and a classical description of networks, which respectively correspond to the Von Neumann and the Shannon entropy.