Social networks, exponential random graph (p ∗) models for

Abstract

Article Outline: Glossary Definition of the Subject Introduction Notation and Terminology Dependence Hypotheses Bernoulli Random Graph (Erdös-Rényi) Models Dyadic Independence Models Markov Random Graphs Simulation and Model Degeneracy Social Circuit Dependence: Partial Conditional Dependence Hypotheses Social Circuit Specifications Estimation Goodness of Fit and Comparisons with Markov Models Further Extensions and Future Directions Bibliography Exponential random graph modelsExponential random graph model, also known as p∗ models, constitute a family of statistical models for socialnetworks. The importance of this modeling framework lies in its capacity to represent social structural effects commonly observed in many human socialnetworks, including general degree-based effects as well as reciprocity and transitivity, and at the node-level, homophily and attribute-basedactivity and popularity effects.The models can be derived from explicit hypotheses about dependencies among network ties. They are parametrized in termsof the prevalence of small subgraphs (configurations) in the network and can be interpreted as describing the combinations of local social processes fromwhich a given network emerges. The models are estimable from data and readily simulated.Versions of the models have been proposed for univariateand multivariate networks, valued networks, bipartite graphs and for longitudinal network data. Nodal attribute data can be incorporated in socialselection models, and through an analogous framework for social influence models. The modeling approach was first proposed in the statistical literature in the mid-1980s, building on previous work in the spatial statistics andstatistical mechanics literature. In the 1990s, the models were picked up and extended by the social networks research community. In this century, withthe development of effective estimation and simulation procedures, there has been a growing understanding of certain inadequacies in the originalform of the models. Recently developed specifications for these models have shown a substantial improvement in fitting real social network data, tothe point where for many network data sets a large number of graph features can be successfully reproduced by the fitted models.