Abstract not found

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 author-recipient 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.

Network models are widely used to represent relational information among interacting units. In studies of social networks, recent emphasis has been placed on random graph models where the nodes usually represent individual social actors and the edges represent the presence of a specified relation between actors. We develop a class of models where the probability of a relation between actors depends on the positions of individuals in an unobserved "social space." Inference for the social space is developed within a maximum likelihood and Bayesian framework, and Markov chain Monte Carlo procedures are proposed for making inference on latent positions and the effects of observed covariates. We present analyses of three standard datasets from the social networks literature, and compare the method to an alternative stochastic blockmodeling approach. In addition to improving upon model fit, our method provides a visual and interpretable model-based spatial representation of social relationships, and improves upon existing methods by allowing the statistical uncertainty in the social space to be quantified and graphically represented.

A large body of work has been devoted to identifying community structure in networks. A community is often though of as a set of nodes that has more connections between its members than to the remainder of the network. In this paper, we characterize as a function of size the statistical and structural properties of such sets of nodes. We define the network community profile plot, which characterizes the “best ” possible community—according to the conductance measure—over a wide range of size scales, and we study over 70 large sparse real-world networks taken from a wide range of application domains. Our results suggest a significantly more refined picture of community structure in large real-world networks than has been appreciated previously. Our most striking finding is that in nearly every network dataset we examined, we observe tight but almost trivial communities at very small scales, and at larger size scales, the best possible communities gradually “blend in ” with the rest of the network and thus become less “community-like.” This behavior is not explained, even at a qualitative level, by any of the commonly-used network generation models. Moreover, this behavior is exactly the opposite of what one would expect based on experience with and intuition from expander graphs, from graphs that are well-embeddable in a low-dimensional structure, and from small social networks that have served as testbeds of community detection algorithms. We have found, however, that a generative model, in which new edges are added via an iterative “forest fire” burning process, is able to produce graphs exhibiting a network community structure similar to our observations.

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A large body of work has been devoted to defining and identifying clusters or communities in social and information networks, i.e., in graphs in which the nodes represent underlying social entities and the edges represent some sort of interaction between pairs of nodes. Most such research begins with the premise that a community or a cluster should be thought of as a set of nodes that has more and/or better connections between its members than to the remainder of the network. In this paper, we explore from a novel perspective several questions related to identifying meaningful communities in large social and information networks, and we come to several striking conclusions. Rather than defining a procedure to extract sets of nodes from a graph and then attempt to interpret these sets as a “real ” communities, we employ approximation algorithms for the graph partitioning problem to characterize as a function of size the statistical and structural properties of partitions of graphs that could plausibly be interpreted as communities. In particular, we define the network community profile plot, which characterizes the “best ” possible community—according to the conductance measure—over a wide range of size scales. We study over 100 large real-world networks, ranging from traditional and on-line social networks, to technological and information networks and

Abstract: This paper describes mathematical models for network evolution when ties (edges) are directed and the node set is xed. Each of these models implies a speci c type of departure from the standard null binomial model. We provide statistical tests that, in keeping with these models, are sensitive to particular types of departures from the null. Each model (and associated test) discussed follows directly from one or more socio-cognitive theories about how individuals alter the colleagues with whom they are likely to interact. The models include triad completion models, degree variance models, polarization and balkanization models, the Holland-Leinhardt models, metric models, and the constructural model. We nd that many of these models, in their basic form, tend asymptotically towards an equilibrium distribution centered at the completely connected network (i.e., all individuals are equally likely to interact with all other individuals) � a fact that can inhibit the development of satisfactory tests. Keywords: triad completion, Holland-Leinhardt model, polarization, degree variance, network evolution, constructuralism

The integrated likelihood (also called the marginal likelihood or the normalizing constant) is a central quantity in Bayesian model selection and model averaging. It is defined as the integral over the parameter space of the likelihood times the prior density. The Bayes factor for model comparison and Bayesian testing is a ratio of integrated likelihoods, and the model weights in Bayesian model averaging are proportional to the integrated likelihoods. We consider the estimation of the integrated likelihood from posterior simulation output, aiming at a generic method that uses only the likelihoods from the posterior simulation iterations. The key is the harmonic mean identity, which says that the reciprocal of the integrated likelihood is equal to the posterior harmonic mean of the likelihood. The simplest estimator based on the identity is thus the harmonic mean of the likelihoods. While this is an unbiased and simulation-consistent estimator, its reciprocal can have infinite variance and so it is unstable in general. We describe two methods for stabilizing the harmonic mean estimator. In the first one, the parameter space is reduced in such a way that the modified estimator involves a harmonic mean of heavier-tailed densities, thus resulting in a finite variance estimator. The resulting

*We acknowledge the helpful comments of the editor and anonymous reviewers. For their encouragement and suggestions on the research, we thank H. Russell Bernard, Linton Freeman, and A. Kimball Romney. We thank Tracy Burkett and Douglas Nigh for making their data available to us.Comparing Networks Across Space and Time, Size and Species We describe and illustrate methodology for comparing networks from diverse settings. Our empirical base consists of 42 networks from four kinds of species (humans, non-human primates, non-primate mammals, and birds) and covering distinct types of relations such as influence, grooming, and agonistic encounters. The general problem is to determine whether networks are similarly structured despite their surface differences. The methodology we propose is generally applicable to the characterization and comparison of network-level social structures across multiple settings, such as different organizations, communities, or social groups, and to the examination of sources of variability in network structure. We first fit a p * model (Wasserman and Pattison 1996) to each network to obtain estimates for effects of six structural properties on the probability of the graph. Then we calculate predicted tie probabilities for each network, using both its own parameter estimates and the estimates from each other network in the collection. Comparison is based on the similarity between sets of predicted tie probabilities. We then use correspondence analysis to represent the similarities among all 42 networks and interpret the resulting configuration using information about the species and relations involved. Results show that similarities among the networks are due more to the kind of relation than to the kind of animal. 2

simulation, model validation, organization theory, network organization, organizational Network organizations offer learning, adaptive and resilient capabilities that are particularly useful in high velocity environments as these capabilities allow the organization to effectively respond to change. The dynamic, evolutionary nature of network organizations affords such advantageous capabilities. Although the advantages of network organizations are well-studied, the risks associated with them are not. Of interest is the study of critical personnel. Understanding criticality within an organization can help improve performance and protect against the risk of loss. But the study of critical personnel has traditionally used static structural representations that do not represent the dynamic nature of network organizations. This thesis advances the study of critical personnel risks in network organizations