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80
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 105 (15 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.
The Network Paradigm in Organizational Research: A Review and Typology
 Journal of Management
, 2003
"... In this paper, we review and analyze the emerging network paradigm in organizational research. We begin with a conventional review of recent research organized around recognized research streams. Next, we analyze this research, developing a set of dimensions along which network studies vary, includi ..."
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Cited by 70 (5 self)
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In this paper, we review and analyze the emerging network paradigm in organizational research. We begin with a conventional review of recent research organized around recognized research streams. Next, we analyze this research, developing a set of dimensions along which network studies vary, including direction of causality, levels of analysis, explanatory goals, and explanatory mechanisms. We use the latter two dimensions to construct a 2by2 table crossclassifying studies of network consequences into four canonical types: structural social capital, social access to resources, contagion, and environmental shaping. We note the rise in popularity of studies with a greater sense of agency than was traditional in network research.
NeighborhoodBased Models for Social Networks
 Sociological Methodology
, 2002
"... Harrison White and several anonymous reviewers for valuable comments on the work. We argue that social networks can be modeled as the outcome of processes that occur in overlapping local regions of the network, termed local social neighborhoods. Each neighborhood is conceived as a possible site of i ..."
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Cited by 54 (4 self)
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Harrison White and several anonymous reviewers for valuable comments on the work. We argue that social networks can be modeled as the outcome of processes that occur in overlapping local regions of the network, termed local social neighborhoods. Each neighborhood is conceived as a possible site of interaction and corresponds to a subset of possible network ties. In this paper, we discuss hypotheses about the form of these neighborhoods, and we present two new and theoretically plausible ways in which neighborhoodbased models for networks can be constructed. In the first, we introduce the notion of a setting structure, a directly hypothesized (or observed) set of exogenous constraints on possible neighborhood forms. In the second, we propose higherorder neighborhoods that are generated, in part, by the outcome of interactive network processes themselves. Applications of both approaches to model construction are presented, and the developments are considered within a general conceptual framework of locale for social networks. We show how assumptions about neighborhoods can be cast within a hierarchy of increasingly complex models; these models represent a progressively greater capacity for network processes to “reach ” across a network through long cycles or semipaths. We argue that this class of models holds new promise for the development of empirically plausible models for networks and networkbased processes. 2 1.
Models for Longitudinal Network Data
 Models and Methods in Social Network Analysis
, 2005
"... This chapter treats statistical methods for network evolution. It is argued that it is most fruitful to consider models where network evolution is represented as the result of many (usually nonobserved) small changes occurring between the consecutively observed networks. Accordingly, the focus is o ..."
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Cited by 33 (6 self)
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This chapter treats statistical methods for network evolution. It is argued that it is most fruitful to consider models where network evolution is represented as the result of many (usually nonobserved) small changes occurring between the consecutively observed networks. Accordingly, the focus is on models where a continuoustime network evolution is assumed although the observations are made at discrete time points (two or more). Three models are considered in detail, all based on the assumption that the observed networks are outcomes of a Markov process evolving in continuous time. The independent arcs model is a trivial baseline model. The reciprocity model expresses effects of reciprocity, but lacks other structural effects. The actororiented model is based on a model of actors changing their outgoing ties as a consequence of myopic stochastic optimization of an objective function. This framework offers the flexibility to represent a variety of network effects. An estimation algorithm is treated, based on a Markov chain Monte Carlo implementation of the method of moments.
Statistical analysis of longitudinal network data with changing composition
, 2003
"... Markov chains can be used for the modeling of complex longitudinal network data. One class of probability models to model the evolution of social networks are stochastic actororiented models for network change proposed by Snijders. These models are continuoustime Markov chain models that are imple ..."
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Cited by 30 (7 self)
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Markov chains can be used for the modeling of complex longitudinal network data. One class of probability models to model the evolution of social networks are stochastic actororiented models for network change proposed by Snijders. These models are continuoustime Markov chain models that are implemented as simulation models. The authors propose an extension of the simulation algorithm of stochastic actororiented models to include networks of changing composition. In empirical research, the composition of networks may change due to actors joining or leaving the network at some point in time. The composition changes are modeled as exogenous events that occur at given time points and are implemented in the simulation algorithm. The estimation of the network effects, as well as the effects of actor and dyadic attributes that influence the evolution of the network, is based on the simulation of Markov chains.
Recovering timevarying networks of dependencies in social and biological studies
 Proc. Nat. Acad. Sci
, 2009
"... A plausible representation of the relational information among entities in dynamic systems such as a living cell or a social community is a stochastic network that is topologically rewiring and semantically evolving over time. While there is a rich literature in modeling static or temporally invaria ..."
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Cited by 29 (8 self)
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A plausible representation of the relational information among entities in dynamic systems such as a living cell or a social community is a stochastic network that is topologically rewiring and semantically evolving over time. While there is a rich literature in modeling static or temporally invariant networks, little has been done toward recovering the network structure when the networks are not observable in a dynamic context. In this paper, we present a new machine learning method called TESLA, which builds on a temporally smoothed l1regularized logistic regression formalism that can be cast as a standard convexoptimization problem and solved efficiently using generic solvers scalable to large networks. We report promising results on recovering simulated timevarying networks, and on reverse engineering the latent sequence of temporally rewiring political and academic social networks from longitudinal data, and the evolving gene networks over more than 4000 genes during the life cycle of Drosophila melanogaster from a microarray time course at a resolution limited only by sample frequency.
Modeling the coevolution of networks and behavior
 In
, 2006
"... A deeper understanding of the relation between individual behavior and individual actions on one hand and the embeddedness of individuals in social structures on the other hand can be obtained by empirically studying the dynamics of individual outcomes and network structure, and how these mutually a ..."
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Cited by 19 (5 self)
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A deeper understanding of the relation between individual behavior and individual actions on one hand and the embeddedness of individuals in social structures on the other hand can be obtained by empirically studying the dynamics of individual outcomes and network structure, and how these mutually affect each other. In methodological terms, this means that behavior of individuals – indicators of performance and success, attitudes and other cognitions, behavioral tendencies – and the ties between them are studied as a social process evolving over time, where behavior and network ties mutually influence each other. We propose a statistical methodology for this type of investigation and illustrate it by an example.
Introduction to Stochastic ActorBased Models for Network Dynamics. Social Networks
, 2009
"... ..."
Small and other worlds: Global network structures from local processes
 American Journal of Sociology
, 2005
"... Using simulation, we contrast global network structures—in particular, small world properties—with the local patterning that generates the network. We show how to simulate Markov graph distributions based on assumptions about simple local social processes. We examine the resulting global structures ..."
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Cited by 18 (1 self)
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Using simulation, we contrast global network structures—in particular, small world properties—with the local patterning that generates the network. We show how to simulate Markov graph distributions based on assumptions about simple local social processes. We examine the resulting global structures against appropriate Bernoulli graph distributions and provide examples of stochastic global “worlds, ” including small worlds, long path worlds, and nonclustered worlds with many fourcycles. In light of these results we suggest a locally specified social process that produces small world properties. In examining movement from structure to randomness, parameter scaling produces a phase transition at a “temperature ” where regular structures “melt ” into stochastically based counterparts. We provide examples of “frozen ” structures, including “caveman ” graphs, bipartite structures, and cyclic structures.