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

Abstract: Exponential-family random graph models (ERGMs) 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 system is a collection of tools for the analysis of network data within an ERGM framework. Many different network properties can be employed as sufficient statistics for ERGMs 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 small, connected, and non-isomorphic induced subgraphs that 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 graphlet into ERGMs. The new model terms of ergm.graphlets package enable both ERG modelling of global structural properties and investigation of relationships between nodal attributes (i.e., covariates) and local topologies around nodes.