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

Transmission of HIV in sexual networks in sub-Saharan Africa and Europe

We are reviewing the literature regarding sexual networks and HIV transmission in sub-Saharan Africa and Europe. On Likoma Island in Malawi, a sexual network was reconstructed using a sociometric survey in which individuals named their sexual partners. The sexual network identified one giant component including half of all sexually active individuals. More than 25% of respondents were linked through independent chains of sexual relations. HIV was more common in the sparser regions of the network due to over-representation of groups with higher HIV prevalence. A study from KwaZulu-Natal in South-Africa collected egocentric data about sexual partners and found that new infections in women in a particular area was associated with the number of life-time partners in men. Data about sexual networks and HIV transmission are not reported in Europe. It is, however, found that the annual number of sexual partners follows a scale-free network. Phylogenetic studies that determine genetic relatedness between HIV isolates obtained from infected individuals, found that patients in the early stages of infections explain a high number of new infections. In conclusion, the limited information that is available suggest that sexual networks play a role in spread of HIV. Obtaining more information about sexual networks can be of benefit for modeling studies on HIV transmission and prevention

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