Co-evolution of networks and quantum dynamics: a generalization of preferential attachment

TL;DR

This paper introduces a co-evolutionary model linking network growth with quantum walk dynamics, resulting in complex networks exhibiting power-law distributions, super-hubs, and small-world properties.

Contribution

It generalizes the preferential attachment model by incorporating quantum dynamics and environmental interactions, offering a novel framework for network evolution.

Findings

Networks with two-modal power-law degree distributions

Presence of super-hubs and finite clustering coefficient

Exhibition of small-world behavior and degree correlations

Abstract

We propose a model of network growth in which the network is co-evolving together with the dynamics of a quantum mechanical system, namely a quantum walk taking place over the network. The model naturally generalizes the Barab\'{a}si-Albert model of preferential attachment and has a rich set of tunable parameters, such as the initial conditions of the dynamics or the interaction of the system with its environment. We show that the model produces networks with two-modal power-law degree distributions, super-hubs, finite clustering coefficient, small-world behaviour and non-trivial degree-degree correlations.