A social partner dance event wants to invite back the "hubs", people whose attendance will induce others to attend next time. One simple way to find these people is simply to count, either exhaustively or by sampling, who dances the most dances. The people who dance a lot can do so because lots of people want to dance with them. Conversely, people who are very picky about who they dance with will probably not be hubs.
At first glance, their seems many ways to game this system, most notably, people arranging to dance only in a clique. However, I suspect those concerns are not too important. With a clique, there will frequently be an odd person out, so everyone in the clique is at a disadvantage. The likelihood, and consequently disadvantage, will be greater for small cliques, inducing larger cliques, or no cliques at all.
Of course, this scheme is nearly equivalent to a popularity contest. Dismiss this not as a problem but a reflection of society.
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