Generating large scale-free networks with the Chung-Lu random graph model

TL;DR

This paper presents a method to generate large scale-free networks with power-law degree distributions using the Chung-Lu model, ensuring theoretical properties like degree control and absence of degree correlations.

Contribution

It provides explicit formulas for model parameters to generate large, realistic scale-free networks with desired properties and guarantees.

Findings

Generated graphs have power-law degree distribution with exponent > 2

Graphs exhibit a giant component and controlled degree properties

Method ensures theoretical properties of the Chung-Lu model are maintained

Abstract

Random graph models are a recurring tool-of-the-trade for studying network structural properties and benchmarking community detection and other network algorithms. Moreover, they serve as test-bed generators for studying diffusion and routing processes on networks. In this paper, we illustrate how to generate large random graphs having a power-law degree distribution using the Chung--Lu model. In particular, we are concerned with the fulfilment of a fundamental hypothesis that must be placed on the model parameters, without which the generated graphs lose all the theoretical properties of the model, notably, the controllability of the expected node degrees and the absence of correlations between the degrees of two nodes joined by an edge. We provide explicit formulas for the model parameters to generate random graphs that have several desirable properties, including a power-law degree distribution with any exponent larger than $2$, a prescribed asymptotic behaviour of the largest and average expected degrees, and the presence of a giant component.