The Weibull as a Model of Shortest Path Distributions in Random Networks
Christian Bauckhage, Kristian Kersting, Bashir Rastegarpanah · 2013
We address the problem of characterizing shortest path histograms of networks in terms of continuous, analytically tractable distributions. Based on a recent model for the expected number of paths between arbitrary vertices in random networks, we establish the Weibull distribution as the corresponding distribution of minimal path lengths. Empirical tests with different graph topologies confirm our theoretical prediction. Our methodology allows for computing non-linear low dimensional embeddings of path histograms for visual analytics.