From regular lattice to scale free network - yet another algorithm

TL;DR

This paper presents a modified Watts-Strogatz algorithm that introduces preferential rewiring based on connectivity demand, resulting in networks with power-law degree distributions, bridging regular lattices and scale-free networks.

Contribution

It proposes a novel modification to the Watts-Strogatz model that produces scale-free networks through threshold-dependent preferential rewiring.

Findings

Networks exhibit power-law degree distribution at specific thresholds.

The modified algorithm effectively transitions from regular to scale-free networks.

Stationary networks maintain degree distribution with power-law decay over large degree intervals.

Abstract

The Watts-Strogatz algorithm transferring a regular lattice to the small world network is modified by introducing preferential rewiring constrained by connectivity demand. The probability to link to/ unlink form a node is dependent on a vertex degree and adjusted by some threshold. For each threshold value there exists a probability at which the resulting stationary network has degree distribution with power-law decay in large interval of degrees.