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Like others it is not clear why you want this.
You need to be clear if the geodesic distances use the weights or not. If you want the length of the path to reflect the weights ie a path length is the sum of the weights of the path and the geodesic is a path with the lowest value then this is standard in UCINET under the reachability routine.
Dear SOCNET members,
I am working on a weighted network and trying to calculate a matrix, each cell of which will be the sum of the weights of all the possible geodesics between any pair of nodes in the network.
Any suggestions on how to calculate such a matrix will be more than valuable.