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<<<-------- Joshua O'Madadhain-------->>>
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> What is it that this is in aid of?
> First: I assume that by "geodesic" you mean "shortest path", in which
> case the lengths of all shortest paths will (by definition) be the
> same, and so this matrix would not be able to distinguish between
> "lots of short paths" and "few long paths". Perhaps this is your
> intent, of course.
> Second: Depending on the topology of your network, there can be an
> exponential number of such paths connecting two vertices.
> So it may be worth reconsidering whether calculating this matrix is a
> good solution to whatever problem you're trying to solve.
If you want a short algorithm see page 63 in
Batagelj, V: Semirings for social networks analysis.
J Math Sociol 19 (1994)1: 53-68
You get two matrices. The answer to your question is a
matrix with elements d[i,j]*c[i,j] .
For larger (some thousands of nodes) networks faster
algorithm can be developed following Brandes' approach.
Vladimir Batagelj, University of Ljubljana, FMF, Department of Mathematics
Jadranska 19, 1000 Ljubljana, Slovenia
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