The block-constrained configuration model

Giona Casiraghi

doi:10.1007/s41109-019-0241-1

Abstract

We provide a novel family of generative block-models for random graphs that naturally incorporates degree distributions: the block-constrained configuration model. Block-constrained configuration models build on the generalized hypergeometric ensemble of random graphs and extend the well-known configuration model by enforcing block-constraints on the edge-generating process. The resulting models are practical to fit even to large networks. These models provide a new, flexible tool for the study of community structure and for network science in general, where modeling networks with heterogeneous degree distributions is of central importance.

Highlights

Stochastic block-models (SBMs) are random models for graphs characterized by group, communities, or block structures
We provide a novel family of generative block-models for random graphs that naturally incorporates degree distributions: the block-constrained configuration model
Before introducing the formulation of the block-constrained configuration model, we provide a brief overview of Generalised hypergeometric ensembles of random graphs (gHypEG)

Summary

Introduction

Stochastic block-models (SBMs) are random models for graphs characterized by group, communities, or block structures. This assumption has the conceptual advantage of not assuming an arbitrary edge generating process, such as the Poisson process considered by DC-SBMs. We define the block-constrained configuration model (BCCM) building on the framework provided by generalized hypergeometric ensembles of random graphs.

Results

Conclusion