We prove that the problem of deciding whether a Nash stable partition exists in an Additively Separable Hedonic Game is NP-complete. We also show that the problem of deciding whether a non trivial Nash stable partition exists in an Additively Separable Hedonic Game with non-negative and symmetric preferences is NP-complete. We motivate our study of the computational complexity by linking Nash stable partitions in Additively Separable Hedonic Games to community structures in networks. Our results formally justify that computing community structures in general is hard.
Theory of Computing Systems, 2009, Vol 45, Issue 4, p. 917-925