Which assignment algorithm should I use?

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I have a single set and I need to generate pairs of two elements among this set. The assignments are all weighted. The matching shall be either constricted or perfect, depends on the results. I guess, I need a weighted matching in general graphs and, as far as I see, Edmonds's algorithm is the correct address. Is that right?

I already implemented Kuhn-Munkres algorithm but I recognized very late that this is only working on bi-partite graphs. Is there maybe a (easy) way to adjust the Kuhn-Munkres algorithm to Edmond's? Otherwise I would go for the Edmond's algorithm.

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