MATLAB - efficient way of computing distances between points in a graph/network using the adjacency matrix and coordinates

Question

I have the network representation in a 2D coordinate space. I have an adjacency matrix Adj(which is sparse) and a coordinate matrix with the x,y values of all the points/nodes/vertices in the graph which are drawn.

I would like to compute as efficiently as possible the distance between these points. I would like to avoid cycling through the entries in the matrix and computing the pairwise distances one by one.

Answer 1

[n, d] = size(coordinate);
assert(d == 2);
resi = sparse(Adj * diag(1:n));
resj = sparse(diag(1:n) * Adj);
res = sparse(zeros(n));
f = find(Adj)
res(f) = sqrt((coordinate(resi(f), 1) - coordinate(resj(f), 1)) .^ 2 + (coordinate(resi(f), 2) - coordinate(resj(f), 2)) .^ 2);

EDIT: Oops, fixed a bug

Clarification: I'm assuming by coordinate matrix you mean like http://www.passagesoftware.net/webhelp/Coordinate_Matrix.htm

EDIT 2: I'm actually not sure whether Adj is a matrix of logicals (or whether you can have a sparse matrix of logicals). I fixed it to sidestep that potential pitfall