A novel configuration model for random graphs with given degree sequence

TL;DR

This paper introduces a new configuration model for random graphs with prescribed degree sequences, providing analytical formulas for degree correlation and clustering, validated by simulations, with potential applications in network analysis.

Contribution

It presents a specific realization of a random graph model where connection probabilities depend on vertex degrees, with analytical insights into degree correlation and clustering.

Findings

Analytical expressions for degree correlation and clustering.

Validation of formulas through numerical simulations.

Discussion of potential applications in network modeling.

Abstract

Recently, random graphs in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices have attracted much attention. Here, we present a specific realization of a class of random network models in which the connection probability between two vertices (i,j) is a specific function of degrees ki and kj. In the framework of the configuration model of random graphs, we find analytical expressions for the degree correlation and clustering as a function of the variance of the desired degree distribution. The expressions obtained are checked by means of numerical simulations. Possible applications of our model are discussed.