Robustness of social networks: Comparative results based on distance distributions

Given a social network, which of its nodes have a stronger impact in determining its structure? More formally: which node-removal order has the greatest impact on the network structure? We approach this well-known problem for the first time in a setting that combines both web graphs and social networks, using datasets that are orders of magnitude larger than those appearing in the previous literature, thanks to some recently developed algorithms and software tools that make it possible to approximate accurately the number of reachable pairs and the distribution of distances in a graph. Our experiments highlight deep differences in the structure of social networks and web graphs, show significant limitations of previous experimental results, and at the same time reveal clustering by label propagation as a new and very effective way of locating nodes that are important from a structural viewpoint.