What exactly do you mean by "two hop distance matrix"?
a) A logical matrix H(i,j) = 1 if the distance between i and j is two?
b) at the most two?
Something like this?
A = [ ...
0 1 1 1 1 0 0 0 0 0
1 0 1 1 1 1 0 0 0 0
1 1 0 0 0 1 1 0 0 0
1 1 0 0 1 1 1 1 0 0
1 1 0 1 0 1 1 1 1 0
0 1 1 1 1 0 0 0 1 1
0 0 1 1 1 0 0 1 1 0
0 0 0 1 1 0 1 0 1 1
0 0 0 0 1 1 1 1 0 0
0 0 0 0 0 1 0 1 0 0 ];
MN = size(A,1);
TwoHopMat = false(MN,MN);
for i = 1:MN
for j = 1:MN
if ( A(i,j) ) % if we can reach this node
% we can reach all it can reach too in two steps
TwoHopMat(i,:) = (TwoHopMat(i,:) | A(:,j)');
end
end
end
% If it is "exactly two" and not "at the most two",
% just remove the original adjacency matrix
% TwoHopMat = xor(TwoHopMat,A);
% If you want it as a double
TwoHopMat = double(TwoHopMat)
Or... shorter
A = logical(A);
TwoHopMatB = zeros(MN,MN);
for i = 1:MN
TwoHopMatB(i,:) = any(A(A(i,:),:),1)
end
EDIT I was originally only checking the upper diagonal. However, with the loop as it is now, this will not work. E.g. A(3,2) == 1, and A(2,6) == 1, so in the end, TwoHopMat(3,6) should be 1. However, if neither 3 nor 6 checks their connection to 2 (upper diagonal), this will get lost.
