Recognizing levels of interaction is one step. But human relationships are not so one-dimensional. Guy I work with, person from Bible group, AA sponsor, girl I snogged once, sister I send cards to once a year but avoid otherwise because we disagree strongly over politics, boss I trust implicitly but don't want to show my off-hour shenanigans to, et cetera, et cetera, et cetera.

Any system which adequately models real relationships will be too complex for usability and any system which is simple enough to have decent usability will only approximate real relationships.

Easy to implement, but

After reading http://news.ycombinator.com/item?id=2795966, i highly doubt that "normal" users want another level of complexity.

And, after all, it can easily be replaced with Circles/Lists :

- Work

- Family

- Golf

- Will Trust for life

- Good friend

- Acquaintances

If you really want to share something with acqaintance from the Golf Club, maybe you just want to email them. Or make more circles/lists :

- Golf : Will Trust for life

- Golf : Good friend

- Golf : Acquaintances

Well, I'm sure social networks like Facebook have already an internal "how good a friend is this person to you?" index for each of your friends, based on how much you interact with them (private messages, invites to events, wall posts, likes, etc.) So adding an extra step to the friend organization process is probably too much work for most people, specially considering people are lazy to even put the context of a friend to begin with (remember that friend lists have kind of failed in terms of user adoption).