Can we compute the graph Laplacian matrix for a directed graph?
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Commented: Souarv De on 16 Mar 2022
How to find graph laplacian matrix of a directed graph?
Christine Tobler on 16 Mar 2022
It depends how you want to define it, there is no one consistent definition of what the graph laplacian of a directed graph is. This wikipedia page https://en.wikipedia.org/wiki/Laplacian_matrix#Definitions_for_simple_graphs lists some options.
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Bruno Luong on 16 Mar 2022
Edited: Bruno Luong on 16 Mar 2022
In this thread I give formula for graph, for digraph you just need to be careful about indegree or outdegree
% TMW example
s = [1 2 2 3 3 3 4 5 5 5 8 8 9];
t = [2 3 4 1 4 5 5 3 6 7 9 10 10];
G = digraph(s,t);
A = G.adjacency;
% Use Laplacian
Din = diag(sum(A,1)); % in degree matrix
Dout = diag(sum(A,2)); % in degree matrix
Lin = Din - A % laplacian matrix
Lout = Dout - A % laplacian matrix
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