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Network-analysis literature is rich in node-centrality measures that quantify the centrality of a node as a function of the (shortest) paths of the network that go through it. Existing work focuses on defining instances of such measures and designing algorithms for the specific combinatorial problems that arise for each instance. In this paper, the authors propose a unifying definition of centrality that subsumes all path-counting based centrality definitions: e.g., stress, betweenness or paths centrality. They also define a generic algorithm for computing this generalized centrality measure for every node and every group of nodes in the network.
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