CCMnet: A Software Package for Network Generation with Congruence Class Models

TL;DR

CCMnet is an R package that generates network ensembles reflecting empirical data uncertainty by defining probability distributions over network property classes, unifying classic models and allowing flexible, non-parametric specifications.

Contribution

Introduces CCMnet, a novel R package that uses a congruence class framework and MCMC sampling to generate flexible network ensembles with specified property uncertainty.

Findings

Successfully generates posterior predictive network ensembles.

Unifies classic network models within a common framework.

Allows arbitrary distributions for network properties.

Abstract

We introduce CCMnet, an R package designed to generate network ensembles that accurately reflect the uncertainty inherent in empirical data. While traditional network modeling often results in ensembles with fixed property values or model-determined levels of variability, CCMnet enables a continuous spectrum of variability for network properties, including edge counts, degree distribution, and mixing patterns. By defining probability distributions directly over congruence classes of networks, the package allows researchers to specify the uncertainty in network properties across the generated ensemble to match a specific sampling design or empirical distribution. Furthermore, this formulation provides a principled framework that encompasses several classic models (e.g., Erd\H{o}s--R\'{e}nyi model, stochastic block models, and certain exponential random graph models) that implicitly share this structural basis, while offering the flexibility to specify arbitrary, even non-parametric, distributions for network properties. CCMnet implements a Markov chain Monte Carlo (MCMC) framework to sample from these models. The utility of the package is illustrated by generating posterior predictive network ensembles representing school friendship networks.