Specification of Exponential-Family Random Graph Models: Terms and Computational Aspects

Abstract

Exponential-family random graph models (ERGMs) represent the processes that govern the formation of links in networks through the terms selected by the user. The terms specify network statistics that are sufficient to represent the probability distribution over the space of networks of that size. Many classes of statistics can be used. In this article we describe the classes of statistics that are currently available in the ergm package. We also describe means for controlling the Markov chain Monte Carlo (MCMC) algorithm that the package uses for estimation. These controls affect either the proposal distribution on the sample space used by the underlying Metropolis-Hastings algorithm or the constraints on the sample space itself. Finally, we describe various other arguments to core functions of the ergm package.

statnet: Software Tools for the Representation, Visualization, Analysis and Simulation of Network Data

“…The main functions within the ergm package are ergm, a function to fit exponential-family random graph models in which the probability of a network is dependent upon a vector of network statistics specified by the user; simulate, a function to simulate random networks using an ERGM; and gof, a function to evaluate the goodness of fit of an ERGM to the data. ergm contains many other functions as well; for a guide to the basic types of functionality these functions provide, see Hunter et al (2008b), Morris, Handcock, and Hunter (2008), and Goodreau et al (2008a) in this volume.…”

“…In other cases, it may require coding a new ergm term using the methods provided for usercoded terms. As discussed in Morris et al (2008), the terms in an ERGM are network statistics that must be calculated for the observed network, and for each step of the MCMC sequence. So every term requires its own algorithm.…”

Bayesian exponential random graph modeling of whole-brain structural networks across lifespan

“…We then compared the observed network with the simulated network based on three global descriptive network characteristics: degree (connectivity), geodic distance (shortest path) and edge-wise shared partners (clustering) from the Bergm package (Caimo and Friel, 2014). Additionally, we implemented the triad census (i.e., subset of motifs), that determines the contributions, as a probability, of one, two or three connections between all possible node triples (Hunter et al, 2009;Morris et al, 2008), and compared these contributions between the observed and simulated networks.…”

Navigating the Range of Statistical Tools for Inferential Network Analysis

“…The major restriction on the specification and inclusion of such effects is that they must be articulable as sums of subnetwork products. See Morris, Handcock, and Hunter (2008) for an extensive treatment of the dependence statistics includable in an ERGM. The ERGM is also special in that, unlike many statistical models, it represents a complete and proper probability model of the entire network and network data-generating process.…”