the only effective way I can see of identifying freindshops is to have an intersection table with both FKS to person.

the problem is how people perceive such friendships

A may think they are frends with B, but B may think they are acquaintences, or colleagues or similar. ie its possible that the realtionship type may not be the same for two people.

eg BillyNoMates is desparate to be friends with anybody
but only one or two real poeple are freinds with BillyNoMates, and most of those are probably forced to becuase they are family or employee