I'm not sure under which 'algorithm' it falls under, but here is the problem:  

I need to match each person to 5 people from the opposite gender (each guy gets 5 girls, each girl gets 5 guys). Not all guy-girl matchings/'edges' are possible, and the edges are weights. Also, I'm not looking for a perfect solution - just a reasonable approximation where most people get as close as possible to 5 matches. 


Any idea how to go about it? The traditional stable marriage and assignment solutions don's work in this case. 


p.s
For context: the real world problem is matching users to girls/guys in their extended social network. 



Polygamous stable marriage/ assignment problem
You can do this as a weighted network-flow problem where each guy is a source of $5$ units, each girl is a sink of $5$ units, and each possible arc has capacity of $1$ unit. You can solve it using linear programming, and the integrality theorem guarantees that a basic optimal solution is in integers.


