Scale free networks from a Hamiltonian dynamics

TL;DR

This paper introduces a fixed-size network model with a Hamiltonian-based dynamics that promotes diverse node connectivity, resulting in equilibrium networks with scale-free degree distributions and hierarchical clustering.

Contribution

It presents a novel fixed-node, fixed-link network model using Hamiltonian dynamics that naturally produces scale-free and hierarchically clustered networks.

Findings

Networks reach equilibrium with broad, power-law degree distributions.

Hierarchical clustering emerges in the same parameter range.

Model differs from growing network models by maintaining fixed size.

Abstract

Contrary to many recent models of growing networks, we present a model with fixed number of nodes and links, where it is introduced a dynamics favoring the formation of links between nodes with degree of connectivity as different as possible. By applying a local rewiring move, the network reaches equilibrium states assuming broad degree distributions, which have a power law form in an intermediate range of the parameters used. Interestingly, in the same range we find non-trivial hierarchical clustering.