Figure : a-1

     Illegal cycles of aggregation between instances.

The one hard rule that UML gives us regarding aggregations is simply this: A whole cannot be its own part. Therefore instances cannot form cycles of aggregations. A single object cannot be an aggregate of itself, two objects cannot be aggregates of each other, three objects cannot form a ring of aggregation, and so on. See Figure a-3

Figure : a-3 , illegal cycle aggregation

I don't find this to be a particularly useful definition. How often am I concerned about making sure that instances form a directed acyclic graph? Not very often. Therefore I find this relationship useless in the kinds of diagrams I draw.