  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.
