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100
Logit models and logistic regressions for social networks. II . . .
, 1999
"... The research described here builds on our previous work by generalizing the univariate models described there to models for multivariate relations. This family, labelled p*, generalizes the Markov random graphs of Frank and Strauss, which were further developed by them and others, building on Besag’ ..."
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Cited by 321 (7 self)
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The research described here builds on our previous work by generalizing the univariate models described there to models for multivariate relations. This family, labelled p*, generalizes the Markov random graphs of Frank and Strauss, which were further developed by them and others, building on Besag’s ideas on estimation. These models were first used to model random variables embedded in lattices by Ising, and have been quite common in the study of spatial data. Here, they are applied to the statistical analysis of multigraphs, in general, and the analysis of multivariate social networks, in particular. In this paper, we show how to formulate models for multivariate social networks by considering a range of theoretical claims about social structure. We illustrate the models by developing structural models for several multivariate networks.
An introduction to exponential random graph (p*) models for social networks.
 Social Networks,
, 2007
"... Abstract 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 determin ..."
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Cited by 195 (4 self)
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Abstract 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, dyadindependent 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.
Models of core/periphery structures
, 1999
"... A common but informal notion in social network analysis and other fields is the concept of a corerperiphery structure. The intuitive conception entails a dense, cohesive core and a sparse, unconnected periphery. This paper seeks to formalize the intuitive notion of a corerperiphery structure and sug ..."
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Cited by 154 (0 self)
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A common but informal notion in social network analysis and other fields is the concept of a corerperiphery structure. The intuitive conception entails a dense, cohesive core and a sparse, unconnected periphery. This paper seeks to formalize the intuitive notion of a corerperiphery structure and suggests algorithms for detecting this structure, along with statistical tests for testing a priori hypotheses. Different .models are presented for different kinds of graphs directed and undirected, valued and nonvalued. In addition, the close relation of the continuous models developed to certain centrality measures is discussed.
Recent developments in exponential random graph (p*) models for social networks
 SOCIAL NETWORKS
, 2006
"... This article reviews new specifications for exponential random graph models proposed by Snijders, Pattison, Robins & Handcock (2006) and demonstrates their improvement over homogeneous Markov random graph models in fitting empirical network data. Not only do the new specifications show improve ..."
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Cited by 120 (15 self)
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This article reviews new specifications for exponential random graph models proposed by Snijders, Pattison, Robins & Handcock (2006) and demonstrates their improvement over homogeneous Markov random graph models in fitting empirical network data. Not only do the new specifications show improvements in goodness of fit for various data sets, they also help to avoid the problem of neardegeneracy that often afflicts the fitting of Markov random graph models in practice, particularly to network data exhibiting high levels of transitivity. The inclusion of a new higher order transitivity statistic allows estimation of parameters of exponential graph models for many (but not all) cases where it is impossible to estimate parameters of homogeneous Markov graph models. The new specifications were used to model a large number of classical smallscale network data sets and showed a dramatically better performance than Markov graph models. We also review three current programs for obtaining maximum likelihood estimates of model parameters and we compare these Monte Carlo maximum likelihood estimates with less accurate pseudolikelihood estimates. Finally we discuss whether homogeneous Markov random graph models may be superseded by the new specifications, and how additional elaborations may further improve model performance.
The Economics of Social Networks.
 In Advances in Economics and Econometrics, Theory and Applications: Ninth World Congress of the Econometric Society.
, 2006
"... Abstract We analyze the problem of optimal monopoly pricing in social networks in order to characterize the influence of the network topology on the pricing rule. It is shown that this influence depends on the type of providers (local versus global monopoly) and of externalities (consumption versus ..."
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Cited by 118 (2 self)
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Abstract We analyze the problem of optimal monopoly pricing in social networks in order to characterize the influence of the network topology on the pricing rule. It is shown that this influence depends on the type of providers (local versus global monopoly) and of externalities (consumption versus price). We identify two situations where the monopolist does not discriminate across nodes in the network (global monopoly with consumption externalities and local monopoly with price externalities) and characterize the relevant centrality index used to discriminate among nodes in the other situations. We also analyze the robustness of the analysis with respect to changes in demand, and the introduction of bargaining between the monopolist and the consumer. JEL Classification Numbers: D85, D43, C69 Keywords: Social Networks, Monopoly Pricing, Network Externalities, Reference Price, Centrality Measures * We dedicate this paper to the memory of Toni CalvóArmengol, a gifted network theorist and a wonderful friend. We thank Coralio Ballester,
Assessing Degeneracy in Statistical Models of Social Networks
 Journal of the American Statistical Association
, 2003
"... discussions. This paper presents recent advances in the statistical modeling of random graphs that have an impact on the empirical study of social networks. Statistical exponential family models (Wasserman and Pattison 1996) are a generalization of the Markov random graph models introduced by Frank ..."
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Cited by 97 (16 self)
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discussions. This paper presents recent advances in the statistical modeling of random graphs that have an impact on the empirical study of social networks. Statistical exponential family models (Wasserman and Pattison 1996) are a generalization of the Markov random graph models introduced by Frank and Strauss (1986), which in turn are derived from developments in spatial statistics (Besag 1974). These models recognize the complex dependencies within relational data structures. A major barrier to the application of random graph models to social networks has been the lack of a sound statistical theory to evaluate model fit. This problem has at least three aspects: the specification of realistic models, the algorithmic difficulties of the inferential methods, and the assessment of the degree to which the graph structure produced by the models matches that of the data. We discuss these and related issues of the model degeneracy and inferential degeneracy for commonly used estimators.
Spatial networks
 PHYSICS REPORTS
, 2010
"... Complex systems are very often organized under the form of networks where nodes and edges are embedded in space. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks, neural networks, are all examples where space is relevant and where topolo ..."
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Cited by 93 (5 self)
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Complex systems are very often organized under the form of networks where nodes and edges are embedded in space. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks, neural networks, are all examples where space is relevant and where topology alone does not contain all the information. Characterizing and understanding
A p* primer: logit models for social networks
 SOCIAL NETWORKS
, 1999
"... A major criticism of the statistical models for analyzing social networks developed by Holland, Leinhardt, and others wHolland, P.W., Leinhardt, S., 1977. Notes on the statistical analysis of social network data; Holland, P.W., Leinhardt, S., 1981. An exponential family of probability distributions ..."
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Cited by 81 (1 self)
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A major criticism of the statistical models for analyzing social networks developed by Holland, Leinhardt, and others wHolland, P.W., Leinhardt, S., 1977. Notes on the statistical analysis of social network data; Holland, P.W., Leinhardt, S., 1981. An exponential family of probability distributions for directed graphs. Journal of the American Statistical Association. 76, pp. 33–65 Ž with discussion.; Fienberg, S.E., Wasserman,
ergm: A Package to Fit, Simulate and Diagnose ExponentialFamily Models for Networks.
, 2003
"... Abstract We describe some of the capabilities of the ergm package and the statistical theory underlying it. This package contains tools for accomplishing three important, and interrelated, tasks involving exponentialfamily random graph models (ERGMs): estimation, simulation, and goodness of fit. M ..."
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Cited by 54 (7 self)
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Abstract We describe some of the capabilities of the ergm package and the statistical theory underlying it. This package contains tools for accomplishing three important, and interrelated, tasks involving exponentialfamily random graph models (ERGMs): estimation, simulation, and goodness of fit. More precisely, ergm has the capability of approximating a maximum likelihood estimator for an ERGM given a network data set; simulating new network data sets from a fitted ERGM using Markov chain Monte Carlo; and assessing how well a fitted ERGM does at capturing characteristics of a particular network data set.
Advances in exponential random graph (p*) models applied to a large social network.
 Social Networks
, 2007
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