4 ms·

The isomorphism is: let the kids be nodes. Between kids x and y, place a red edge if x and y are friends, or place a blue edge if x and y are not friends.

• varjag 8y ago
  Psychologic findings are statistical. Cliques do not form perfectly reliably; there are kids who would have no friends, kids who have common friend but hate each other, or yes all six could be friends indeed. R(3,3) doesn't seem universal enough here to be touted as "isomorphism"; it is not giving any particular insight except the most trivial (that child cliques sometimes can be represented as monochromatic sets of a complete graph). Am certain one can do a number of other graph-theoretic or algebraic relationships here with zero insight or predictive force.
  • xamuel 8y ago
    R(3,3) doesn't say a clique necessarily forms. It says a clique forms or an anti-clique forms (or both). If all six are friends, then there are (6 choose 3) cliques. If all six hate each other, there are (6 choose 3) anti-cliques. If one kid is hated by everyone, that in some sense decreases the odds of a clique but simultaneously increases the chances of an anti-clique, and R(3,3)=6 guarantees that in some sense these increases/decreases balance each other out.
• mattkrause 8y ago
  My point, above, is that this isn't necessarily a good abstraction. The edges could be directed (A considers B a friend, B does not consider A a friend). The graph may not actually be complete (maybe absence of friendship is different from non-friendship), and so on. So yes, if kids' friendships form a complete undirected graph, then sure, your result is not at all surprising. But maybe they don't.