I think that the "polyamory" part relates to multiple and loves. If you have multiple loves, you are poly. If your partner has more than one love, your "relationship" is poly, even if YOU are not, and you are only involved with that one person.
I suppose there is something to be said for the concept of "you are essentially sleeping with everyone your partner has ever slept with", if you are talking about STD risk, and how, conceptually, that can be applied to a poly chain of relationships.
CuriouslyPoly, it sounds like you are seeking a solid, defined, delineated way of defining a poly relationship. AS if it needs to "end" somewhere, and be somewhat contained. But as the other posters here have said, many poly relationships have overlap or connections. Just as friendships do, and blended families when people marry, divorce, and remarry. The relationship parts may change, but dont necessarily disappear.
London spoke of how some people try to make poly seem safer or more "palatable" by having strict boundaries or definitions for their relationships. But ultimately, by its very nature, poly is not really something that is contained in nice neat structures.
Yes, some people are involved in V relationships which connect to other relationships. The people who participate in those relationships will define them as they wish, either as a V, an N, a network, or as non-monogamous. I personally define the poly part as love and intentional committment to the relationship. (Committment is not always a lifetime thing, but it means, to me, you are important enough for me to make an effort to include you in my life in a significant way, and I will be there for you if you need me to be. It can include family, romantic, friends, and even work colleagues. It is not limiting and it is also not exclusive.)
If a closed, polyfidelitous relationship makes the most sense to you, then that is what you should seek out for yourself. There are many people who love that way and are very happy. It is simply that others want those close, intense or primary type relationships AND others as well. I have my husband and my long term boyfriend, they are my poly relationships. If I have a snuggle bunny or two on the side, those people may be poly, and we may choose to call our interactions poly, even though it may be in a very casual "see-you-once-a-year" kind of way. It is still poly.
Just keep swimming, Just keep swimming... ~ Dori
Willow ~ 44yo bi woman, married to Bear (formerly known as TB) for 18 years
Bear-Maybe poly/maybe mono straight man, still feeling it out
Armadillo (formerly known as BF) - currently out of the picture. Depression is evil...