On the classic aristophanic notion of romantic love two lovers unite. Unification is a transitive relation.* So on this notion of love all polyamoretic love graphs are complete.** In fact, the union of all polyamoretic love graphs is complete. But this is cleary absurd. It thus follows that the classic aristophanic notion of romantic love is incompatible with polyamory.
(*) If person A unites with person B and person B unites with person C, then person A unites with person C.
(**) A polyamoretic love graph is a graph that connects a person to all of his or her lovers.
A complete graph is a graph in which each pair of graph vertices is connected by an edge.