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The fractional chromatic index is computed via linear programming. Its Sage implementation is pretty clear and documented line-by-line, you can read and adapt it to the weighted case by typing:

G.fractional_chromatic_index??

The fractional chromatic index is computed via linear programming. programming and duality. Its Sage implementation is pretty clear and documented line-by-line, you can read and adapt it to the weighted case by typing:

G.fractional_chromatic_index??