ergm.graphlets: A Package for ERG Modeling Based on Graphlet Statistics

Abstract

Exponential-family random graph models are probabilistic network models that are parametrized by sufficient statistics based on structural (i.e., graph-theoretic) properties. The ergm package for the R statistical computing environment is a collection of tools for the analysis of network data within an exponential-family random graph model framework. Many different network properties can be employed as sufficient statistics for exponential- family random graph models by using the model terms defined in the ergm package; this functionality can be expanded by the creation of packages that code for additional network statistics. Here, our focus is on the addition of statistics based on graphlets. Graphlets are classes of small, connected, induced subgraphs that can be used to describe the topological structure of a network. We introduce an R package called ergm.graphlets that enables the use of graphlet properties of a network within the ergm package of R. The ergm.graphlets package provides a complete list of model terms that allows to incorporate statistics of any 2-, 3-, 4- and 5-node graphlets into exponential-family random graph models. The new model terms of the ergm.graphlets package enable both exponential-family random graph modeling of global structural properties and investigation of relationships between node attributes (i.e., covariates) and local topologies around nodes.