# Can we compute the graph Laplacian matrix for a directed graph?

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How to find graph laplacian matrix of a directed graph?

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### Accepted Answer

Christine Tobler
on 16 Mar 2022

### More Answers (1)

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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