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Closeness centrality is a fundamental centrality measure that quantifies how centrally located a node is, within a network, based on its total distances to all other nodes. In this paper, we first derive a set of linear inequality and equality constraints, which are distributed in nature, that characterize closeness centrality in lieu of its original definition. We then use these constraints to develop...
Betweenness centrality is a fundamental centrality measure that quantifies how important a node or an edge is, within a network, based on how often it lies on the shortest paths between all pairs of nodes. In this paper, we develop a scalable distributed algorithm, which enables every node in a network to estimate its own betweenness and the betweenness of edges incident on it with only local interaction...
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