An introduction to exponential random graph (p*) models for social networks

By Garry Robins, P. Pattison, Yuval Kalish, Dean Lusher. 2007

2,078 citations recorded by the source corpus.

This article provides an introductory summary to the formulation and application of exponential random graph models for social networks. The possible ties among nodes of a network are regarded as random variables, and assumptions about dependencies among these random tie variables determine the general form of the exponential random graph model for the network. Examples of different dependence assumptions and their associated models are given, including Bernoulli, dyad-independent and Markov random graph models. The incorporation of actor attributes in social selection models is also reviewed. Newer, more complex dependence assumptions are briefly outlined. Estimation procedures are discussed, including new methods for Monte Carlo maximum likelihood estimation. We foreshadow the discussion taken up in other papers in this special edition: that the homogeneous Markov random graph models of Frank and Strauss [Frank, O., Strauss, D., 1986. Markov graphs. Journal of the American Statistical Association 81, 832–842] are not appropriate for many observed networks, whereas the new model specifications of Snijders et al. [Snijders, T.A.B., Pattison, P., Robins, G.L., Handock, M. New specifications for exponential random graph

Subfields: Management Science and Operations Research, Statistical and Nonlinear Physics

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Citations in the corpus

GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models (2018, background): “…and stochastic block models) (Erd ˝ os & R ´ enyi, 1959; Leskovec et al., 2010; Albert & Barab ´ asi, 2002; Airoldi et al., 2008; Leskovec et al., 2007; Robins et al., 2007) are hand-engineered to model a particular family of graphs, and thus do not have the capacity to directly learn the…”
Network structure and institutional complexity in an ecology of water management games (2014, background): “Study design: the ecology of water management games in San Francisco Bay, California SF Bay is one of the most important coastal regions on the west coast of North America, and involves numerous environmental issues, actors, and policy institutions (Norgaard et al. 2009).”
Private analysis of graph structure (2011, background): “For example, the subgraph counts f 2 (cid:2) , f 3 (cid:2) , and f (cid:2) , as well as the number of edges, f edge , are suﬃcient statistics for several popular exponential random graph models (ERGM) (e.g., [11, 12, 6]).”
Culture, Cognition, and Collaborative Networks in Organizations (2011, methodology): “This approach represents a rather stringent test of goodness-of-fit: the model is considered to fit well if it reproduces features of the network that were not used to construct it (for further information on the guidelines for fitting ERGMs, see Morris, Handcock, and Hunter 2008; O’Malley and Marsd”
Exponential random graph models for multilevel networks (2013, methodology): “We can apply the current ERGM specifications for one-mode networks (Snijders et al., 2006; Robins et al., 2007b, 2009) to look at within level network structures, given other effects in the model. zQ (x) are the network statistics for structural effects within the bipartite affiliation network.”
Understanding network formation in strategy research: Exponential random graph models (2016, methodology): “To implement ERGMs, it is important to understand the dependence assumptions that define the ways in which the observed ties may be related (Brandes et al., 2013; Pattison and Robins, 2002; Robins et al., 2007a).”
The dynamics of animal social networks: analytical, conceptual, and theoretical advances (2014, positive): “Exponential random graph modeling (ERGM, or p* modeling) is a well-developed statistical technique, used extensively in the social sciences, that enables examination of the underlying mechanisms of network factors and processes that generate nonrandom network structures (Anderson et al. 1999; Robins”
The Alignment of the Informal and Formal Organizational Supports for Reform: Implications for Improving Teaching in Schools (2010, background): “Social selection models focus on predicting the existence of particular relationships between actors from a range of characteristics, including individuals’ prior interactions with one another (Frank and Fahrbach, 1999; Leenders, 1997; Robins et al., 2007).”
ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks. (2008, methodology): “The ergm package for R (R Development Core Team 2007), a cornerstone of the statnet suite of packages for statistical network analysis, provides tools for modeling networks based on a well-studied class of models called exponential-family random graph models (ERGMs) or p-star models (Holland and Lei”
Comparing Brain Networks of Different Size and Connectivity Density Using Graph Theory (2010, methodology): “The incidences of the statistics are given by a set of parameters h m that can be determined via maximizing the likelihood of the model [65].”
Statistical Models for Social Networks (2011, background): “An example is the elaboration of this type of model for directed networks by Robins et al. (2009), where many different dependence structures are possible because directions of ties can be combined in so many ways.”
Structural balance in the social networks of a wild mammal (2013, methodology): “To further substantiate our findings, we used exponentialfamily random graph models (ERGM; Wasserman & Pattison 1996; Robins et al. 2007).”
The analysis of social networks (2008, background): “, within actors, dyads, triads, or tetrads (Robins et al. 2005). Examples of such regularities are actor-level tendencies to produce and/or attract ties, dyadic tendencies toward reciprocity, and triadic tendencies toward closure or transitivity. Relational models may also incorporate attribute data”
Comparing Community Structure to Characteristics in Online Collegiate Social Networks (2008, background): “, [35]), statistically fitting an underlying model for the presence of links.”