I see KingNothing's point. There could theoretically be groups of relationships that cannot be represented without crossing lines (or without requiring a third dimension to the graph).
Following OfficeShredders lead, I was about to ask what the simplest group of relationships is. OfficeShredder went for the group of five, but he missed the simpler one: 4 people. i.e. a tetrahedron.
4 people, all of whom have had romantic relationships with each other, cannot be represented in only 2 dimensions without crossing lines.
sheds light on the answer to KingNothing's point. This simplest relationship requires some statistically highly unlikely connections. 4 people all having had relationships with each other is unlikely enough, but to do so, it requires a minimum
of two same-sex relationships.