Differentially Private Exponential Random Graphs

We propose methods to release and analyze synthetic graphs in order to protect privacy of individual relationships captured by the social network. Proposed techniques aim at fitting and estimating a wide class of exponential random graph models (ERGMs) in a differentially private manner, and thus offer rigorous privacy guarantees. More specifically, we use the randomized response mechanism to release networks under $\epsilon$-edge differential privacy. To maintain utility for statistical inference, treating the original graph as missing, we propose a way to use likelihood based inference and Markov chain Monte Carlo (MCMC) techniques to fit ERGMs to the produced synthetic networks. We demonstrate the usefulness of the proposed techniques on a real data example.Comment: minor edit

From network ties to network structures: exponential random graph models of interorganizational relations

Theoretical accounts of network ties between organizations emphasize the interdependence of individual intentions, opportunities, and actions embedded in local configurations of network ties. These accounts are at odds with empirical models based on assumptions of independence between network ties. As a result, the relation between models for network ties and the observed network structure of interorganizational fields is problematic. Using original fieldwork and data that we have collected on collaborative network ties within a regional community of hospital organizations we estimate newly developed specifications of Exponential Random Graph Models (ERGM) that help to narrow the gap between theories and empirical models of interorganizational networks. After controlling for the main factors known to affect partner selection decisions, full models in which local dependencies between network ties are appropriately specified outperform restricted models in which such dependencies are left unspecified and only controlled for statistically. We use computational methods to show that networks based on empirical estimates produced by models accounting for local network dependencies reproduce with accuracy salient features of the global network structure that was actually observed. We show that models based on assumptions of independence between network ties do not. The results of the study suggest that mechanisms behind the formation of network ties between organizations are local, but their specification and identification depends on an accurate characterization of network structure. We discuss the implications of this view for current research on interorganizational networks, communities, and fields