This is currently written so that one person can either have a relation with someone or not. If you expand it to have n possible relations (including not knowing them) there are (n^6+3*n^3-n^2-3*n)/6 possibilities. For example:
One relationship: 0 possibilities (in this case, not knowing each other is the only possible relation, and if nobody knows each other, it's not a love triangle).
- Two relationships: 13 possibilities.
- Three relationships: 132 possibilities.
- Four relationships: 710 possibilities.
- Five relationships: 2660 possibilities.
See the discussion
According to OEIS
, there are 13 connected digraphs with 3 nodes, which correspond to the 13 Love Triangles
in the main article. For four people, however, there are 199
possible relationship networks. And if you're looking at a Love Dodecahedron
... well, the sequence only goes up to 13 in the database, and it's a 38-digit number.