Abstract
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.