Finite Mixtures of ERGMs for Modeling Ensembles of Networks

Ensembles of networks arise in many scientific fields, but there are few statistical tools for inferring their generative processes, particularly in the presence of both dyadic dependence and cross-graph heterogeneity. To fill in this gap, we propose characterizing network ensembles via finite mixtures of exponential family random graph models, a framework for parametric statistical modeling of graphs that has been successful in explicitly modeling the complex stochastic processes that govern the structure of edges in a network. Our proposed modeling framework can also be used for applications such as model-based clustering of ensembles of networks and density estimation for complex graph distributions. We develop a Metropolis-within-Gibbs algorithm to conduct fully Bayesian inference and adapt a version of deviance information criterion for missing data models to choose the number of latent heterogeneous generative mechanisms. Simulation studies show that the proposed procedure can recover the true number of latent heterogeneous generative processes and corresponding parameters. We demonstrate the utility of the proposed approach using an ensemble of political co-voting networks among U.S. Senators

Formal Hierarchies and Informal Networks: How Organizational Structure Shapes Information Search in Local Government

Attention to informal communication networks within public organizations has grown in recent decades. While research has documented the role of individual cognition and social structure in understanding information search in organizations, this article emphasizes the importance of formal hierarchy. We argue that the structural attributes of bureaucracies are too important to be neglected when modeling knowledge flows in public organizations. Empirically, we examine interpersonal information seeking patterns among 143 employees in a small city government, using exponential random graph modeling (ERGM). The results suggest that formal structure strongly shapes information search patterns while accounting for social network variables and individual level perceptions. We find that formal status, permission pathways, and departmental membership all affect the information search of employees. Understanding the effects of organizational structure on information search networks will offer opportunities to improve information flows in public organizations via design choices.Comment: Accepted for publication in Journal of Public Administration Research and Theor

Consistent structure estimation of exponential-family random graph models with block structure

We consider the challenging problem of statistical inference for exponential-family random graph models based on a single observation of a random graph with complex dependence. To facilitate statistical inference, we consider random graphs with additional structure in the form of block structure. We have shown elsewhere that when the block structure is known, it facilitates consistency results for $M$-estimators of canonical and curved exponential-family random graph models with complex dependence, such as transitivity. In practice, the block structure is known in some applications (e.g., multilevel networks), but is unknown in others. When the block structure is unknown, the first and foremost question is whether it can be recovered with high probability based on a single observation of a random graph with complex dependence. The main consistency results of the paper show that it is possible to do so under weak dependence and smoothness conditions. These results confirm that exponential-family random graph models with block structure constitute a promising direction of statistical network analysis