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Mixed membership stochastic block models for relational data with application to proteinprotein interactions
 In Proceedings of the International Biometrics Society Annual Meeting
, 2006
"... We develop a model for examining data that consists of pairwise measurements, for example, presence or absence of links between pairs of objects. Examples include protein interactions and gene regulatory networks, collections of authorrecipient email, and social networks. Analyzing such data with p ..."
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Cited by 336 (45 self)
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We develop a model for examining data that consists of pairwise measurements, for example, presence or absence of links between pairs of objects. Examples include protein interactions and gene regulatory networks, collections of authorrecipient email, and social networks. Analyzing such data with probabilistic models requires special assumptions, since the usual independence or exchangeability assumptions no longer hold. We introduce a class of latent variable models for pairwise measurements: mixed membership stochastic blockmodels. Models in this class combine a global model of dense patches of connectivity (blockmodel) and a local model to instantiate nodespecific variability in the connections (mixed membership). We develop a general variational inference algorithm for fast approximate posterior inference. We demonstrate the advantages of mixed membership stochastic blockmodels with applications to social networks and protein interaction networks.
Markov Chain Monte Carlo Estimation of Exponential Random Graph Models
 Journal of Social Structure
, 2002
"... This paper is about estimating the parameters of the exponential random graph model, also known as the p # model, using frequentist Markov chain Monte Carlo (MCMC) methods. The exponential random graph model is simulated using Gibbs or MetropolisHastings sampling. The estimation procedures consider ..."
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Cited by 153 (17 self)
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This paper is about estimating the parameters of the exponential random graph model, also known as the p # model, using frequentist Markov chain Monte Carlo (MCMC) methods. The exponential random graph model is simulated using Gibbs or MetropolisHastings sampling. The estimation procedures considered are based on the RobbinsMonro algorithm for approximating a solution to the likelihood equation.
Evolution of Sociology Freshmen into a Friendship Network
 Journal of Mathematical Sociology
, 2003
"... In this paper we both describe and analyze the meeting process and the evolution of a friendship network among sociology freshmen in the Netherlands. We develop a theory that explains how changes in the network structure depend on one or more of four main effects: proximity, visible similarity, inv ..."
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Cited by 21 (4 self)
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In this paper we both describe and analyze the meeting process and the evolution of a friendship network among sociology freshmen in the Netherlands. We develop a theory that explains how changes in the network structure depend on one or more of four main effects: proximity, visible similarity, invisible similarity, and network opportunity. We formulate expectations with regard to what factors are important at what stages of the friendship development, making a distinction between ‘meeting ’ and ‘mating. ’ To some extent, the results
Heider vs. Simmel: Emergent features in dynamic structure
 In Statistical Network Analysis: Models, Issues, and New Directions
, 2007
"... Abstract. Heider’s balance theory is ubiquitous in the field of social networks as an explanation for why we so frequently observe symmetry and transitivity in social relations. We propose that Simmelian tie theory could explain the same phenomena without resorting to motivational tautologies that ..."
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Cited by 19 (1 self)
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Abstract. Heider’s balance theory is ubiquitous in the field of social networks as an explanation for why we so frequently observe symmetry and transitivity in social relations. We propose that Simmelian tie theory could explain the same phenomena without resorting to motivational tautologies that characterize psychological explanations. Further, while both theories predict the same equilibrium state, we argue that they suggest different processes by which this equilibrium is reached. We develop a dynamic exponential random graph model (ERGM) and apply it to the classic panel data collected by Newcomb to empirically explore these two theories. We find strong evidence that Simmelian triads exist and are stable beyond what would be expected through Heiderian tendencies in the data. 1 Heider’s Balance Theory One of the central questions in the field of network analysis is: How do networks form? A cornerstone to our understanding of this process from a structural point
Conditional Maximum Likelihood Estimation under Various Specifications of Exponential Random Graph Models
 Frank. University of Stockholm: Department of Statistics
, 2002
"... This paper considers only models with such a conditioning ..."
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Cited by 15 (9 self)
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This paper considers only models with such a conditioning
Comparing Social Networks: Size, Density, and Local Structure
"... This paper demonstrates limitations in usefulness of the triad census for studying similarities among local structural properties of social networks. A triad census succinctly summarizes the local structure of a network using the frequencies of sixteen isomorphism classes of triads (subgraphs of th ..."
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Cited by 15 (0 self)
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This paper demonstrates limitations in usefulness of the triad census for studying similarities among local structural properties of social networks. A triad census succinctly summarizes the local structure of a network using the frequencies of sixteen isomorphism classes of triads (subgraphs of three nodes). The empirical base for this study is a collection of 51 social networks measuring different relational contents (friendship, advice, agonistic encounters, victories in fights, dominance relations, and so on) among a variety of species (humans, chimpanzees, hyenas, monkeys, ponies, cows, and a number of bird species). Results show that, in aggregate, similarities among triad censuses of these empirical networks are largely explained by nodal and dyadic properties – the density of the network and distributions of mutual, asymmetric, and null dyads. These results remind us that the range of possible networklevel properties is highly constrained by the size and density of the network and caution should be taken in interpreting higher order structural properties when they are largely explained by local network features. 1
Setting in social networks: A measurement model
 Sociological Methodology
, 2003
"... A class of statistical models is proposed that aims to recover latent settings structures in social networks. Settings may be regarded as clusters of vertices. The measurement model is based on two assumptions. (1) The observed network is generated by hierarchically nested latent transitive structu ..."
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Cited by 14 (2 self)
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A class of statistical models is proposed that aims to recover latent settings structures in social networks. Settings may be regarded as clusters of vertices. The measurement model is based on two assumptions. (1) The observed network is generated by hierarchically nested latent transitive structures, expressed by ultrametrics, and (2) the expected tie strength decreases with ultrametric distance. The approach could be described as modelbased clustering with an ultrametric space as the underlying metric to capture the dependence in the observations. Bayesian methods as well as maximumlikelihood methods are applied for statistical inference. Both approaches are implemented using Markov chain Monte Carlo methods. 1.
A Bayesian approach toward finding communities and their evolutions in dynamic social networks
 In SDM’09: proceedings of the 2009 SIAM international
, 2009
"... Although a large body of work are devoted to finding communities in static social networks, only a few studies examined the dynamics of communities in evolving social networks. In this paper, we propose a dynamic stochastic block model for finding communities and their evolutions in a dynamic social ..."
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Cited by 14 (2 self)
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Although a large body of work are devoted to finding communities in static social networks, only a few studies examined the dynamics of communities in evolving social networks. In this paper, we propose a dynamic stochastic block model for finding communities and their evolutions in a dynamic social network. The proposed model captures the evolution of communities by explicitly modeling the transition of community memberships for individual nodes in the network. Unlike many existing approaches for modeling social networks that estimate parameters by their most likely values (i.e., point estimation), in this study, we employ a Bayesian treatment for parameter estimation that computes the posterior distributions for all the unknown parameters. This Bayesian treatment allows us to capture the uncertainty in parameter values and therefore is more robust to data noise than point estimation. In addition, an efficient algorithm is developed for Bayesian inference to handle large sparse social networks. Extensive experimental studies based on both synthetic data and reallife data demonstrate that our model achieves higher accuracy and reveals more insights in the data than several stateoftheart algorithms.