From Scale-free to Erdos-Renyi Networks

TL;DR

This paper introduces a model that smoothly transitions between scale-free and Erdos-Renyi networks, enabling analysis of how structural heterogeneity affects network properties and percolation behavior.

Contribution

The paper presents a new one-parameter network model bridging scale-free and Erdos-Renyi networks, with analytical and numerical analysis of the transition.

Findings

The model accurately describes the transition between network types.

Structural heterogeneity significantly influences percolation thresholds.

Analytical results match extensive numerical simulations.

Abstract

We analyze a model that interpolates between scale-free and Erdos-Renyi networks. The model introduced generates a one-parameter family of networks and allows to analyze the role of structural heterogeneity. Analytical calculations are compared with extensive numerical simulations in order to describe the transition between these two important classes of networks. Finally, an application of the proposed model to the study of the percolation transition is presented.