Are laplacians for directed graphs used in any algorithms ? For example laplacians for the undirected graphs are used in algorithms such as spectral clustering.
2026-03-25 05:06:53.1774415213
Usefulness of Laplacians for directed graphs
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I know nothing about spectral clustering, but here is one use of Laplacians in directed graphs I do know.
Kirchhoff's matrix tree theorem gives that the number of spanning trees on a directed (multi)graph in the determinant of the reduced Laplacian. With the appropriate definitions the the theorem also holds for directed graphs, see here. As the link shows you can weight your edges how ever you like and count "weighted directed spanning trees" with a specified root.