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Many basic questions in the social network literature center on the distribution of aggregate structural properties within and across populations of networks. Such questions are of increasing relevance given the growing availability of network data suitable for meta-analytic studies, as well as the rise of study designs that involve the collection of data on multiple networks drawn from a larger population. Despite this, little work has been done on model-based inference for the properties of graph populations, or on methods for comparing such populations. Here, we attempt to rectify this gap by introducing a family of techniques that combines an existing approach to the identification of structural biases in network data (the use of conditional uniform graph quantiles) with strategies drawn from nonparametric Bayesian analysis. Conditional uniform graph quantiles are the quantiles of an observed structural property in the reference distribution produced by evaluating that property over all graphs with certain fixed characteristics (e.g., size or density). These quantiles have long been used to measure the extent to which a property of interest on a single network deviates from what would be expected given that network's other characteristics. The methods introduced here employ such quantile information to allow for principled inference regarding the distribution of structural biases within (and comparison across) populations of networks, given data sampled at the network level. The data requirements of these methods are minimal, thus making them well-suited to meta-analytic applications for which complete network data (as opposed to summary statistics) are often unavailable. The structural biases inferred using these methods can be expressed in terms of posterior predictives for familiar and easily communicated quantities, such as p-values. In addition to the methods themselves, we present algorithms for posterior simulation from this model class, illustrating their use with applications to the analysis of social structure within urban communes and radio communications among emergency personnel. We also discuss how this approach may applied to quantiles arising from other reference distributions, such as those obtained using general exponential-family random graph models.

General random graphs (i.e., stochastic models for networks incorporating heterogeneity and/or dependence among edges) are increasingly in wide use in the study of social and other networks, but few techniques other than simulation have been available for studying their behavior. On the other hand, random graphs with independent edges (i.e., the Bernoulli graphs) are well-studied, and a large literature exists regarding their properties. In this paper, we demonstrate a method for leveraging this knowledge by constructing families of Bernoulli graphs that bound the behavior of an arbitrary random graph in a well-defined sense. By studying the behavior of these Bernoulli graph bounds, we can thus constrain the properties of a given random graph. We illustrate the utility of this approach via application to several problems from the social network literature, including identifying degeneracy in Markov graph models, studying the potential impact of tie formation mechanisms on epidemic potential in sexual contact networks, and robustness testing of inhomogeneous Bernoulli models based on geographical covariates. Practical heuristics for assessing bound tightness and guidance for use in theoretical and methodological applications are also discussed.

Social behavior over short time scales is frequently understood in terms of actions, which can be thought of as discrete events in which one individual emits a behavior directed at one or more other entities in his or her environment (possibly including himself or herself). Here, we introduce a highly flexible framework for modeling actions within social settings, which permits likelihood-based inference for behavioral mechanisms with complex dependence. Examples are given for the parameterization of base activity levels, recency, persistence, preferential attachment, transitive/cyclic interaction, and participation shifts within the relational event framework. Parameter estimation is discussed both for data in which an exact history of events is available, and for data in which only event sequences are known. The utility of the framework is illustrated via an application to dynamic modeling of responder radio communications during the early hours of the World Trade Center disaster.

A formal framework is introduced for a general class of assignment systems that can be used to characterize a range of social phenomena. An exponential family of distributions is developed for modeling such systems, allowing for the incorporation of both attributional and relational covariates. Methods are shown for simulation and inference using the location system model. Two illustrative applications (occupational stratification and residential settlement patterns) are presented, and simulation is employed to show the behavior of the location system model in each case; a third application, involving occupancy of positions within an organization, is used to demonstrate inference for the location system. By leveraging established results in the fields of social network analysis, spatial statistics, and statistical mechanics, it is argued that sociologists can model complex social systems without sacrificing inferential tractability.

A common problem in sociology, psychology, biology, geography, and management science is the comparison of dyadic relational structures (i.e., graphs). Where these structures are formed on a common set of elements, a natural question that arises is whether there is a tendency for elements that are strongly connected in one set of structures to be more—or less—strongly connected within another set. We may ask, for instance, whether there is a correspondence between golf games and business deals, trade and warfare, or spatial proximity and genetic similarity. In each case, the data for such comparisons may be continuous or discrete, and multiple relations may be involved simultaneously (e.g., when comparing multiple measures of international trade volume with multiple types of political interactions). We propose here an exponential family of permutation models that is suitable for inferring the direction and strength of association among dyadic relational structures. A linear-time algorithm is shown for MCMC simulation of model draws, as is the use of simulated draws for maximum likelihood estimation (MCMC-MLE) and/or estimation of Monte Carlo standard errors. We also provide an easily performed maximum pseudo-likelihood estimation procedure for the permutation model family, which provides a reasonable means of generating seed models for the MCMC-MLE procedure. Use of the modeling framework is demonstrated via an application involving relationships among managers in a high-tech firm.