Local entropy and nonextensivity of networks ensembles

TL;DR

This paper theoretically proves the presence of nonextensivity in binary and weighted network ensembles, highlighting a key difference from traditional statistical physics models due to local entropy's nonlinear behavior.

Contribution

It provides the first theoretical proof of nonextensivity in network ensembles, based on local entropy's nonlinear change with network growth.

Findings

Nonextensivity exists in both microcanonical and canonical network ensembles.

Local entropy exhibits nonlinear change when nodes are added.

Nonextensivity distinguishes network ensembles from traditional models.

Abstract

Nonextensivity is foreseeable in network ensembles, as heterogeneous interactions generally exist in complex networked systems that need to be described by network ensembles. But this nonextensivity has not been literatured proved yet. In this work, the existence of nonextensivity in the binary and weighted network ensembles is theoretically proved for the first time (both in the microcanonical and canonical ensemble) based on the finding of the local entropy's nonlinear change when new nodes are added to the network ensembles. This proof also shows that the existence of nonextensivity is the main difference between the network ensembles and other traditional models in statistical physics (Ising model).