A measure of centrality in cyclic diffusion processes: Walk-betweenness.

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. We also find that village leaders with high walk-betweenness are more likely to accelerate the rate of microfinance take-up among their followers, outperforming other traditional centrality measures in regression analyses.