How can I sum edge weight in selected vertices ?

Dear All:

My question should be easy but I've confused about it. For example I have matrix which indicate the weight between nodes.

edgeMarix = [
     0    1     0    2    0    4
     1    0     7    9    3    0
     0    7     0    9    0    5
     2    9     9    0    3    0
     0    3     0    3    0    5
     4    0     5    0    5    0

now I want to calculate the sum of edges in 2(or n) different group in such a way for example first Partition is nodes 1,3,4 and the other is 2,5,6 So obviously with respect to given matrix the total edge of first group should be : (1,3)+(1,4)+(3,4) = 0 + 2 + 9 = 11 and second one (2,5)+(2,6)+(5,6) = 3 + 0 + 5 = 8

so how I could do it in matlab :)? thanks in advance

Answer 1

[the cyclist]

edgeMarix = [
     0    1     0    2    0    4
     1    0     7    9    3    0
     0    7     0    9    0    5
     2    9     9    0    3    0
     0    3     0    3    0    5
     4    0     5    0    5    0];

partition = {[1 3 4],[2 5 6]};

numberPartitions = numel(partition);

s = cell(1,numberPartitions);
for np = 1:numberPartitions
    s{np} = 0;
    currentPartition = partition{np};
    numberIndices = numel(currentPartition);
    for i1 = 1:numberIndices
    for i2=i1:numberIndices
        s{np} = s{np} + edgeMarix(currentPartition(i1),currentPartition(i2));
    end
    end
end

[mahdi]

Thanks so much man ;) have a nice weekend :D

Answer 2

[Roger Stafford]

 % Define a group
 G = [1,3,4];

 % calculate the weight between nodes
 C = nchoosek(G,2);
 W = sum(edgeMarix(sub2ind(size(C),C(:,1),C(:,2))));

[mahdi]

thanks first but the G(could be n groups with different members) and edgeMatrix just given.

how could I do it automatically? :p

[Roger Stafford]

Just put above code in an appropriate for-loop.

 % Let each row of G be a group of indices for 'edgeMarix'.
 n = size(G,1);
 W = zeros(n,1);
 for k = 1:n;
   C = nchoosek(G(k,:),2);
   W(k) = sum(edgeMarix(sub2ind(size(C),C(:,1),C(:,2))));
 end

This assumes all groups in G have the same number of elements. Otherwise you should store them in a cell array and make the obvious changes in the above code.