MATLAB: A = [ 1 2 1;1 3 1;1 4 1;2 5 2;3 5 3;4 5 4] ; For above matrix first i need out put like all possible path like 1-2-5 and its total weight (1+2 =3); path 1-3-5 and its total weight (1+3 = 4), Path 1-4-5 and its total weight (1+4 =5);

data structure

Finding Longest Path in Directed Acyclic Graph

Best Answer

You can try this:
A = [ 1 2 1;1 3 1;1 4 1;2 5 2;3 5 3;4 5 4];
cntr = 1;
path = [];
for i = 1:length(A)
    path(i).startNode = A(i, 1);
    path(i).path = [A(i, 2)];
    path(i).weight = A(i, 3);
end
for i = 1:length(A)
    for j = 1:length(A)
        if(path(j).path(end) == A(i, 1))
            path(j).path = [path(j).path,  A(i, 2)];
            path(j).weight = path(j).weight +  A(i, 2);
        end
    end
end
But this assumes that your paths are at most of length two. Otherwise you might want to consider a recursive approach.
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