A measure of centrality in cyclic diffusion processes: walk-betweenness

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**Abstract:** Unlike many traditional measures of centrality based on paths that do not allow any repeated nodes or lines, we propose a new measure of centrality based on walks, walk-betweenness, that allows any number of repeated nodes or lines. To illustrate the value of walk-betweenness, we examine the transmission of syphilis in Chicago area and the diffusion of microfinance in 43 rural Indian villages. Walk-betweenness allows us to identify hidden bridging communities in Chicago that were essential in the transmission dynamics. Also, village leaders with high walk-betweenness increase the rate of microfinance participation among their followers, outperforming other traditional centrality measures in the regression analysis.

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