  Betweenness centrality lies at the core of both transport and structural
vulnerability properties of complex networks, however, it is computationally
costly, and its measurement for networks with millions of nodes is near
impossible. By introducing a multiscale decomposition of shortest paths, we
show that the contributions to betweenness coming from geodesics not longer
than L obey a characteristic scaling vs L, which can be used to predict the
distribution of the full centralities. The method is also illustrated on a
real-world social network of 5.5*10^6 nodes and 2.7*10^7 links.
