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Given a connected graph G=(V,E), the closeness centrality of a vertex v is defined as n-1/∑_w ∈ V d(v,w). This measure is widely used in the analysis of real-world complex networks, and the problem of selecting the k most central vertices has been deeply analysed in the last decade. However, this problem is computationally not easy, especially for large networks: in the first part of the paper, we prove that it is not solvable in time Ø(|E|^2-ϵ) on directed graphs, for any constant ϵ>0, underarXiv:1704.01077v2 fatcat:gc32wvmmdzhczka6rv7h3c7ajy