From Help, the procedure StableMarriage was an element of the Combinatorica, but it is available in the built-in FindIndependentEdgeSet since Mathematica 10.

But it is not clear from the documentation how to use FindIndependentEdgeSet as a Gale-Shapley algorithm straightforwardly. So, the procedure FindIndependentEdgeSet can find an independent edge set and, for weighted graphs, maximal total-valued independent edge set. But this is no the same as a stable matching. How to solve it?

Explicitly: The input of the StableMarriage is a pair of permutations describing male and female preferences. But that is not acceptable input for FindIndependentEdgeSet procedure

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    $\begingroup$ I think that the fact that you got multiple upvotes but no answers indicates that how to do this is not at all obvious (if possible at all!). I would contact Wolfram Support and ask about it. They should be able to contact whoever wrote that documentation page and ask for clarifications. $\endgroup$ – Szabolcs Mar 2 at 9:35

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