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<<<-------- Joshua O'Madadhain-------->>>
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>
> Emmanouil:
>
> 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.

  Vlado


-- 
Vladimir Batagelj, University of Ljubljana, FMF, Department of Mathematics
  Jadranska 19, 1000 Ljubljana, Slovenia
http://vlado.fmf.uni-lj.si

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