Trivia / Triang Relations

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 for details.

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.