Boley, DanielRanjan, GyanZhang, Zhi-Li2020-09-022020-09-022010-03-08https://hdl.handle.net/11299/215823The expected commute times for a strongly connected directed graph are related to an asymmetric Laplacian matrix as a direct extension to similar well known formulas for undirected graphs. We show the close relationships between the asymmetric Laplacian and the so-called Fundamental matrix. We give bounds for the commute times in terms of the stationary probabilities for a random walk over the graph together with the asymmetric Laplacian and show how this can be approximated by a symmetrized Laplacian derived from a related weighted undirected graph.en-USReport