  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.
