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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.
Inference in Curved Exponential Family Models for Networks
 Journal of Computational and Graphical Statistics
, 2006
"... Network data arise in a wide variety of applications. Although descriptive statistics for networks abound in the literature, the science of fitting statistical models to complex network data is still in its infancy. The models considered in this article are based on exponential families; therefore, ..."
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Cited by 80 (11 self)
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Network data arise in a wide variety of applications. Although descriptive statistics for networks abound in the literature, the science of fitting statistical models to complex network data is still in its infancy. The models considered in this article are based on exponential families; therefore, we refer to them as exponential random graph models (ERGMs). Although ERGMs are easy to postulate, maximum likelihood estimation of parameters in these models is very difficult. In this article, we first review the method of maximum likelihood estimation using Markov chain Monte Carlo in the context of fitting linear ERGMs. We then extend this methodology to the situation where the model comes from a curved exponential family. The curved exponential family methodology is applied to new specifications of ERGMs, proposed by Snijders et al. (2004), having nonlinear parameters to represent structural properties of networks such as transitivity and heterogeneity of degrees. We review the difficult topic of implementing likelihood ratio tests for these models, then apply all these modelfitting and testing techniques to the estimation of linear and nonlinear parameters for a collaboration network between partners in a New England law firm.
Birds of a feather, or friend of a friend?: USING EXPONENTIAL RANDOM GRAPH MODELS TO . . .
, 2009
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Advances in exponential random graph (p*) models applied to a large social network.
 Social Networks
, 2007
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Mapping change in large networks
 PLoS ONE
"... Change is the very nature of interaction patterns in biology, technology, economy, and science itself: The interactions within and between organisms change; the air, ground, and sea traffic change; the global financial flow changes; and the scientific research front changes. With increasingly availa ..."
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Cited by 38 (3 self)
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Change is the very nature of interaction patterns in biology, technology, economy, and science itself: The interactions within and between organisms change; the air, ground, and sea traffic change; the global financial flow changes; and the scientific research front changes. With increasingly available data, networks and clustering tools have become important tools to comprehend instances of these largescale structures. But blind to the difference between noise and trends in the data, these tools alone must fail when used to study change. Only if we can assign significance to the partition of single networks can we distinguish structural changes from fluctuations and assess how much confidence should we have in the changes. Here we show that bootstrap resampling accompanied by significance clustering provides a solution to this problem. We use the significance clustering to realize de Solla Price’s vision of mapping the change in science. Network analysis provides tools for understanding social and biological systems with numerous and diverse interacting components. For large networks, we need ways to highlight the important features while simplifying the overall structure. Researchers have developed a suite of
Philosophy and the practice of Bayesian statistics
, 2010
"... A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually ..."
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Cited by 37 (8 self)
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A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypotheticodeductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework.
Beyond and Below Racial Homophily: ERG Models of a Friendship Network Documented on Facebook
 AMERICAN JOURNAL OF SOCIOLOGY
, 2010
"... A notable feature of U.S. social networks is their high degree of racial homogeneity, which is often attributed to racial homophily— the preference for associating with individuals of the same racial background. The authors unpack racial homogeneity using a theoretical framework that distinguishes b ..."
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Cited by 19 (0 self)
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A notable feature of U.S. social networks is their high degree of racial homogeneity, which is often attributed to racial homophily— the preference for associating with individuals of the same racial background. The authors unpack racial homogeneity using a theoretical framework that distinguishes between various tie formation mechanisms and their effects on the racial composition of networks, exponential random graph modeling that can disentangle these mechanisms empirically, and a rich new data set based on the Facebook pages of a cohort of college students. They first show that racial homogeneity results not only from racial homophily proper but also from homophily among coethnics of the same racial background and from balancing mechanisms such as the tendency to reciprocate friendships or to befriend the friends of friends, which both amplify the homogeneity effects of homophily. Then, they put the importance of racial homophily further into perspective by comparing its effects to those of other mechanisms of tie formation. Balancing, propinquity based on coresidence, and homophily regarding nonracial categories (e.g., students from “elite ” backgrounds or those from particular states) all influence the tie formation process more than does racial homophily.
Community extraction for social networks
, 2010
"... Analysis of networks and in particular discovering communities within networks has been a focus of recent work in several fields, with applications ranging from citation and friendship networks to food webs and gene regulatory networks. Most of the existing community detection methods focus on parti ..."
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Cited by 19 (1 self)
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Analysis of networks and in particular discovering communities within networks has been a focus of recent work in several fields, with applications ranging from citation and friendship networks to food webs and gene regulatory networks. Most of the existing community detection methods focus on partitioning the entire network into communities, with the expectation of many ties within communities and few ties between. However, many networks contain nodes that do not fit in with any of the communities, and forcing every node into a community can distort results. Here we propose a new framework that focuses on community extraction instead of partition, extracting one community at a time. The main idea behind extraction is that the strength of a community should not depend on ties between members of other communities, but only on ties within that community and its ties to the outside world. We show that the new extraction criterion performs well on simulated and real networks, and establish asymptotic consistency of our method under the block model assumption.
Review of statistical network analysis: models, algorithms, and software
 STATISTICAL ANALYSIS AND DATA MINING
, 2012
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Discovering long range properties of social networks with multivalued timeinhomogeneous models
 In AAAI
, 2010
"... The current methods used to mine and analyze temporal social network data make two assumptions: all edges have the same strength, and all parameters are timehomogeneous. We show that those assumptions may not hold for social networks and propose an alternative model with two novel aspects: (1) the ..."
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Cited by 12 (2 self)
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The current methods used to mine and analyze temporal social network data make two assumptions: all edges have the same strength, and all parameters are timehomogeneous. We show that those assumptions may not hold for social networks and propose an alternative model with two novel aspects: (1) the modeling of edges as multivalued variables that can change in intensity, and (2) the use of a curved exponential family framework to capture timeinhomogeneous properties while retaining a parsimonious and interpretable model. We show that our model outperforms traditional models on two realworld social network data sets.