Assessing Centrality Without Knowing Connections

We consider the privacy-preserving computation of node influence in distributed social networks, as measured by egocentric betweenness centrality (EBC). Motivated by modern communication networks spanning multiple providers, we show for the first time how multiple mutually-distrusting parties can successfully compute node EBC while revealing only differentially-private information about their internal network connections. A theoretical utility analysis upper bounds a primary source of private EBC error---private release of ego networks---with high probability. Empirical results demonstrate practical applicability with a low 1.07 relative error achievable at strong privacy budget $\epsilon=0.1$ on a Facebook graph, and insignificant performance degradation as the number of network provider parties grows.

Differentially-Private Two-Party Egocentric Betweenness Centrality

We describe a novel protocol for computing the egocentric betweenness centrality of a node when relevant edge information is spread between two mutually distrusting parties such as two telecommunications providers. While each node belongs to one network or the other, its ego network might include edges unknown to its network provider. We develop a protocol of differentially-private mechanisms to hide each network's internal edge structure from the other; and contribute a new two-stage stratified sampler for exponential improvement to time and space efficiency. Empirical results on several open graph data sets demonstrate practical relative error rates while delivering strong privacy guarantees, such as 16% error on a Facebook data set.