I have some social network data in which I'd like to identify people who belong to a group of 5 friends. These are users who are friends with 4 other people who all are also friends with each other.
In the graph sense, this task involves identifying components of the graph where each node has an edge between every other node in the component and where the component contains at least 5 nodes.
Is there a well known algorithm to do this? I was looking at measures like centrality, clustering coefficients, and strongly connected components but none of those are quite what I want.