A profile of an individual is genealogically defined if there is a source that will lead to the identification of his/her parents, a source for each spouse, and a source for each child.
In practice, you may be looking at a profile of Jane who married John Doe. You may think Jane was the child of Alice and Bob Smith. Suppose you even have a birth record showing Alice and Bob had a daughter Jane Smith born in 1700, another record showing *some* Jane Smith married John Doe in 1720, and a gravestone of Jane Doe right next to John Doe's from which you can infer her birth year was 1700. If you're in this position, you're lucky, but this doesn't prove that John Doe's wife was the Jane born to Alice and Bob.
On the other hand, if you find a land record signed by both Alice and Bob Smith at a reasonable time and place in which they convey land to their daughter Jane Doe, wife of John Doe, out of love for their daughter, that is, in my opinion, stronger evidence of the connection than the combination of the birth and marriage records and gravestone I mentioned above.
Is there a word used for these "connecting" records that name an individual and at least two of either their parents, spouses, or children?