Generating random networks that consist of a single connected component with a given degree distribution

TL;DR

This paper introduces a method to generate random networks with a specified degree distribution that are guaranteed to be a single connected component, extending existing models by controlling component size and correlations.

Contribution

The authors develop a novel construction method for single-component networks with prescribed degree distributions, incorporating degree correlations and disassortativity.

Findings

Networks exhibit degree-degree correlations and disassortativity.

Method works for ternary, exponential, and power-law degree distributions.

Networks are guaranteed to be a single connected component.

Abstract

We present a method for the construction of ensembles of random networks that consist of a single connected component with a given degree distribution. This approach extends the construction toolbox of random networks beyond the configuration model framework, in which one controls the degree distribution but not the number of components and their sizes. Unlike configuration model networks, which are completely uncorrelated, the resulting single-component networks exhibit degree-degree correlations. Moreover, they are found to be disassortative, namely high-degree nodes tend to connect to low-degree nodes and vice versa. We demonstrate the method for single-component networks with ternary, exponential and power-law degree distributions.