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Centrality, which quantifies the "importance" of individual nodes, is amongthe most essential concepts in modern network theory. As there are many ways inwhich a node can be important, many different centrality measures are in use.Here, we concentrate on versions of the common betweenness and it closenesscentralities. The former measures the fraction of paths between pairs of nodesthat go through a given node, while the latter measures an average inversedistance between a particular node and all other nodes. Both centralities onlyconsider shortest paths (i.e., geodesics) between pairs of nodes. Here wedevelop a method, based on absorbing Markov chains, that enables us tocontinuously interpolate both of these centrality measures away from thegeodesic limit and toward a limit where no restriction is placed on the lengthof the paths the walkers can explore. At this second limit, the interpolatedbetweenness and closeness centralities reduce, respectively, to the well-knownit current betweenness and resistance closeness (information) centralities. Themethod is tested numerically on four real networks, revealing complex changesin node centrality rankings with respect to the value of the interpolationparameter. Non-monotonic betweenness behaviors are found to characterize nodesthat lie close to inter-community boundaries in the studied networks.

Absorbing Random Walks Interpolating Between Centrality Measures on Complex Networks