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Does the current implementation of IGMinimumEdgeColoring and IGChromaticIndex in IGraph/M work with multigraphs? I recall reading something to the effect of the contrary but I can’t find that source again.

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Yes, edge colouring functions are intended to work with multigraphs. Do note that the current implementation is not quite as efficient as for simple graphs.

Mathematica itself has the annoying limitation that it is not possible to set separate edge properties for parallel edges. Therefore, it is not possible to visualize the edge colouring in the same straightforward way as for simple graphs. However, the colouring can be computed and the functions you mention are not affected by the problem. The visualization will, unfortunately, have to be done manually.

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  • $\begingroup$ Thank you very much for your very useful answer ... I wonder if the implementation of graphs and networks can be done differently so that what can be done with it can still be done, but also, so that this problem does not prop up ... would you have any ideas? One could contact the developer’s and suggest ... $\endgroup$ – EGME Jun 1 at 19:44
  • $\begingroup$ @EGME Generally, it helps if more than one user writes to Wolfram Support to request a feature ... $\endgroup$ – Szabolcs Jun 1 at 19:51
  • $\begingroup$ Right. The problem is to actually propose a solution, so I was wondering if you can imagine one. I think that once a good solution is at hand, I think a proposal will not only be taken seriously, but if everything fits into the development scheme, something will be done about it. I think I can almost guarantee this. At the moment, M is lacking some graph theoretical functionality, and has some quite good one in. It is probably time for them to augment this functionality in ways that are important to the G+N community. $\endgroup$ – EGME Jun 1 at 19:56

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