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 nearly 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 versus $L$, which can be used to predict the distribution of the full centralities. The method is also illustrated on a real-world social network of $5.5\times {10}^6$ nodes and $2.7\times {10}^7$ links.

• Received 2 March 2010

DOI:https://doi.org/10.1103/PhysRevLett.105.038701