Quantum statistics in complex networks

TL;DR

This paper explores quantum statistical properties in complex networks, introducing a model with mixed quantum statistics that accounts for node energy differences and rewiring, revealing inhomogeneous connectivity behavior.

Contribution

It presents a novel network model combining bosonic and fermionic statistics with energy-dependent node behavior and rewiring dynamics.

Findings

Nodes below threshold energy increase connectivity

Nodes above threshold energy decrease connectivity

The system exhibits inhomogeneous connectivity patterns

Abstract

In this work we discuss the symmetric construction of bosonic and fermionic networks and we present a case of a network showing a mixed quantum statistics. This model takes into account the different nature of nodes, described by a random parameter that we call energy, and includes rewiring of the links. The system described by the mixed statistics is an inhomogemeous system formed by two class of nodes. In fact there is a threshold energy $\epsilon_s$ such that nodes with lower energy $(\epsilon<\epsilon_s)$ increase their connectivity while nodes with higher energy $(\epsilon>\epsilon_s)$ decrease their connectivity in time.