Connection probability for random graphs with given degree sequence

TL;DR

This paper derives analytical formulas for connection probabilities in the classical and directed configuration models, enhancing understanding of random graphs with specified degree sequences.

Contribution

It introduces the expanding coefficient method to analytically compute connection probabilities for both undirected and directed configuration models.

Findings

Derived analytical expression for connection probability in undirected configuration model.

Extended the method to obtain connection probability in directed configuration model.

Provided insights into the structure of random graphs with given degree sequences.

Abstract

Recently, the classical configuration model for random graphs with given degree distribution has been extensively used as a null model in contraposition to real networks with the same degree distribution. In this paper, we briefly review the applications of this model and derive analytical expression for connection probability by the expanding coefficient method. We also use our expanding coefficient method to obtain the connection probability for the directed configuration model.