Distributed estimation of closeness centrality

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 a scalable distributed algorithm, which enables nodes in a network to cooperatively estimate their individual closeness with only local interaction and without any centralized coordination, nor high memory usages. Finally, we evaluate the algorithm performance via extensive simulation, showing that it yields closeness estimates that are 91% accurate in terms of ordering, on random geometric, Erdös-Rényi, and Barabási-Albert graphs.