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Can the centrality measures in Mathematica (e.g., degree, betweenness, edge betweenness) be adjusted for weight on the edges, where weights represent the volume of an item (say, in Kg)? This would be for directed graphs.

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  • $\begingroup$ The notation for kilogrammes is "kg", not "Kg". Capitalization matters in the SI system. Kilogrammes measure mass, not volume. $\endgroup$
    – Szabolcs
    Commented May 2 at 11:57

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The answer depends on which specific measure you want to compute.

The IGraph/M package does contain weighted implementations for most measures where Mathematica ignores weights.

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  • $\begingroup$ we would use mass on the edges $\endgroup$
    – user42700
    Commented May 2 at 12:00
  • $\begingroup$ Is there an example with IGraph/M you could share, with edge weights as kg (mass)? $\endgroup$
    – user42700
    Commented May 2 at 12:02
  • $\begingroup$ The documentation contains many examples, have you looked at it? Edge weights are arbitrary numerical quantities: it makes no difference what the unit of measurement is. That said, read up on the definition of the various centralities, and how they use weights. It makes no sense to use masses where weights are interpreted as edge/path length (e.g. betweenness, closeness). $\endgroup$
    – Szabolcs
    Commented May 2 at 12:07
  • $\begingroup$ so masses are not captured as an edge weight; just edge/path length $\endgroup$
    – user42700
    Commented May 2 at 13:21
  • $\begingroup$ I'm sorry, I do not understand your question. I suggest reading up on each centrality measure you want to compute. Make sure you understand how they work before you use them. $\endgroup$
    – Szabolcs
    Commented May 2 at 15:33

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