Statistical networks emerging from link-node interactions

TL;DR

This paper introduces a statistical network model where node-link interactions lead to phase transitions, clustering, and bistability, with applications in magnetism and opinion dynamics.

Contribution

It presents a novel model combining Ising spins and network formation, revealing how node-link interactions influence phase transitions and network structure.

Findings

At high temperatures, the network behaves like an Erdős-Rényi graph.

Low temperatures induce spontaneous node ordering and network clustering.

The model predicts a shift to first-order percolation transition with hysteresis.

Abstract

We study a model for a statistical network formed by interactions between its nodes and links. Each node can be in one of two states (Ising spin up or down) and the node-link interaction facilitates linking between the like nodes. For high temperatures the influence of the nodes on the links can be neglected, and we get the Ising ferromagnet on the random (Erdos-Renyi) graph. For low temperatures the nodes get spontaneously ordered. Due to this, the connectivity of the network enhances and links having a common node are correlated. The emerged network is clustered. The node-link interaction shifts the percolation threshold of the random graph to much smaller values, and the very percolation transition can become of the first order: the giant cluster coexist with the unconnected phase leading to bistability and hysteresis. The model can be applied to the striction phenomena in magnets and to studying opinion formation in the sociophysical context.