# How to generate a sparse matrix for a given array?

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Benson Gou on 24 May 2021
Commented: Benson Gou on 25 May 2021
Dear All,
I want to generate a sparse matrix B for a given array A. A contains two columns of indecis. For example,
A = [1 3;
1 4;
2 3;
2 5;
3 5;
4 5]
The sparse matrix B should be as follows:
B = [ 2 0 -1 -1 0;
0 2 -1 0 -1;
-1 -1 2 0 0;
-1 0 0 2 -1;
0 -1 -1 -1 3]
The characteristics of B:
1. Sum of each row is zero.
2. If we consider matrix A gives the information of edges of a graph, B(i,i) = sum of number of edges, B(i,j) = -1 if there is an edge between i and j.
Thanks a lot.
Benson

Matt J on 25 May 2021
Edited: Matt J on 25 May 2021
B=laplacian( graph(A(:,1),A(:,2)) );
Matt J on 25 May 2021

the cyclist on 24 May 2021
Here is one way:
A = [1 3;
1 4;
2 3;
2 5;
3 5;
4 5];
d = max(A(:));
B = sparse(A(:,1),A(:,2),-1,d,d) + sparse(A(:,2),A(:,1),-1,d,d);
for ii = 1:d
B(ii,ii) = -sum(B(ii,:));
end
disp(B)
(1,1) 2 (3,1) -1 (4,1) -1 (2,2) 2 (3,2) -1 (5,2) -1 (1,3) -1 (2,3) -1 (3,3) 3 (5,3) -1 (1,4) -1 (4,4) 2 (5,4) -1 (2,5) -1 (3,5) -1 (4,5) -1 (5,5) 3
Benson Gou on 25 May 2021
Hi, the Cyclist,
Thanks a lot for your great help. You have a good day!
Benson