# Laplacian matrix of directed graph

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The 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.sition of the graph Laplacian, can not be directly used on directed graphs, since the adjacency matrix is asymmet-ric Stankovic, Dakovi´ ´c, and Sejdi c (2019). A straightfor-´ ward method is to symmetrize directed graphs into undi-rected graphs. Unfortunately, treating directed graphs as undirected graphs will overlook the asymmetric nature and