There is a Bipartite Matching domain name, BipartiteMatching.com which could be used for the theory and application of this technique for various purposes unrelated to social technology, but currently it is redirected to a subdomain of SocialTechnology.ca because the sole reason for creating this site was for a discussion of its application in social situations.
Specifically, it is one of the mathematical methods a person might use in improving their social environment. Perhaps the most important aspect of a person’s social environment is a spouse or lover, and that should be a bipartite relationship. Each person old enough for such a relationship should have only one, or no more than one at a time — such is conventional wisdom, and I personally agree with it.
That is a bipartite match. Of more interest is a complete bipartite match in which each person has such a relationship. That is much better for society as a whole, and is my primary interest.
Other relationships which should perhaps be bipartite include that of best friend and that of mentor and protege.
Creating good social relationships of all kinds is the subject of social network optimization. The most important method for linking people to create a good social network is bipartite matching, but it is utterly dependent on good data. For a discussion of this data, see the Linear Profiles website.