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

Ravi Goyal, Victor De Gruttola, Natasha K. Martin, Lior Rennert, Jukka-Pekka Onnela

TL;DR

CCMnet is introduced, an R package designed to generate network ensembles that accurately reflect the uncertainty inherent in empirical data, and implements a Markov chain Monte Carlo framework to sample from these models.

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., Erdős--Rényi 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.

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

TL;DR

CCMnet is introduced, an R package designed to generate network ensembles that accurately reflect the uncertainty inherent in empirical data, and implements a Markov chain Monte Carlo framework to sample from these models.

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., Erdős--Rényi 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.
Paper Structure (23 sections, 3 equations, 3 figures, 2 tables)

This paper contains 23 sections, 3 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Constraints on Network Properties
  3. Hard-Constraints on Network Properties
  4. Soft-Constraints on Network Properties
  5. Spectrum of Constraints on Network Properties
  6. Congruence Class Models
  7. Congruence Classes of Networks
  8. Congruence Class Models
  9. Simple Examples
  10. CCMnet Software Architecture
  11. Interface and Input Validation
  12. Computational Backend
  13. Output and Diagnostics
  14. Network Properties Implemented
  15. Topological-based Network Properties
  16. ...and 8 more sections

Figures (3)

  • Figure 1: Conceptual illustration of network uncertainty. All the plots show distributions for a network property, which can represent edge count, degree distribution, or mixing patterns. In Panel A, the two distributions represents variance under a hard-constraint (dark blue) and a soft-constraint where the variance is fixed (green). Panel B shows the flexibility of CCMs to model a broad range of uncertainty for the same network property (red curves). Panel C demonstrates the continuous spectrum of uncertainty by mapping the network property distributions in Panels A and B to where they reside on the spectrum.
  • Figure 2: The space of all $2^{{4 \choose 2}} = 64$ undirected binary graphs of size $n=4$, partitioned into congruence classes based on edge count. Each cell represents a unique graph, with colors and red boundaries indicating the seven distinct congruence classes (0 to 6 edges).
  • Figure 3: The modular architecture of CCMnet. The model is specified via the R interface, where input validation occurs. The Markov chain Monte Carlo (MCMC) algorithm is implemented in the C backend. Resulting network and MCMC diagnostics are then returned to R for analysis.