The biggest group of friends together?

Question

I am trying to find the largest group of friends who theoretically get along with each other, i.e. each person in the group must know at least 50% of the other people in the group.

I am trying to come up with an algorithm for this that does not last funny; Facebook API / cross-server conversation is pretty slow as it is.

I thought I could start with a friend who has the most common friends with me, and then add people to the group one by one. But who will I choose next?

Just interested in theory, no code needed.

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Edit: When I said “theory” that I actually meant that the next logical step in plain English :) I was hoping I could do it in the afternoon, but I think it is a little more complicated than I expected, and I I’m not sure I want to spend several weeks thinking about a heavy schedule theory. However, maybe someone else will find this interesting.

Answer 1

MIT worked for some time on social graphic transformation. Although he used mobile phone data, clustering algorithms and other systems should still be applied, although they are built using different input data and criteria.

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Answer 2

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Answer 3

This is broader, but see if it helps to get ideas.