Exponential random graph model parameter estimation for very large directed networks

Abstract

Exponential random graph models (ERGMs) are widely used for modeling social networks observed at one point in time. However the computational difficulty of ERGM parameter estimation has limited the practical application of this class of models to relatively small networks, up to a few thousand nodes at most, with usually only a few hundred nodes or fewer. In the case of undirected networks, snowball sampling can be used to find ERGM parameter estimates of larger networks via network samples, and recently published improvements in ERGM network distribution sampling and ERGM estimation algorithms have allowed ERGM parameter estimates of undirected networks with over one hundred thousand nodes to be made. However the implementations of these algorithms to date have been limited in their scalability, and also restricted to undirected networks. Here we describe an implementation of the recently published Equilibrium Expectation (EE) algorithm for ERGM parameter estimation of large directed networks. We test it on some simulated networks, and demonstrate its application to an online social network with over 1.6 million nodes.

arXiv commentMinor correction of discussion of coverage and Type II error rate

References in corpus (12)

• Power-law distributions in empirical data
• Scale-free networks are rare
• Modeling social networks from sampled data
• SNAP: A General Purpose Network Analysis and Graph Mining Library
• Fitting heavy tailed distributions: the poweRlaw package
• Exponential-Family Models of Random Graphs: Inference in Finite-, Super-, and Infinite Population Scenarios
• On the Concept of Snowball Sampling
• Evolution of the digital society reveals balance between viral and mass media influence
• Large-scale estimation of random graph models with local dependence
• Fast Maximum Likelihood estimation via Equilibrium Expectation for Large Network Data
• A Simple Algorithm for Scalable Monte Carlo Inference
• Why (and When and How) Contrastive Divergence Works

Cited by in corpus (7)

• Exponential Random Graph models for Little Networks
• Democratic Governance and International Research Collaboration: A Longitudinal Analysis of the Global Science Network
• Testing biological network motif significance with exponential random graph models
• The Homophily Principle in Social Network Analysis
• ALAAMEE: Open-source software for fitting autologistic actor attribute models
• Improving exponential-family random graph models for bipartite networks
• Deep Generative Modeling in Network Science with Applications to Public Policy Research