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The neighbourhood function N_G(t) of a graph G gives, for each t ∈ N, the number of pairs of nodes x, y such that y is reachable from x in less that t hops. The neighbourhood function provides a wealth of information about the graph [10] (e.g., it easily allows one to compute its diameter), but it is very expensive to compute it exactly. Recently, the ANF algorithm [10] (approximate neighbourhood function) has been proposed with the purpose of approximating N_G(t) on large graphs. We describe a breakthrough improvement over ANF in terms of speed and scalability. Our algorithm, called HyperANF, uses the new HyperLogLog counters [5] and combines them efficiently through broadword programming [8]; our implementation uses talk decomposition to exploit multi-core parallelism. With HyperANF, for the first time we can compute in a few hours the neighbourhood function of graphs with billions of nodes with a small …