Could you clarify what you mean by "various ways a circle can be formed"? I think there is only one way: governance.
Also, AFAIK there is no difference between a circle and a sub circle (eg. every circle is a sub circle of the general circle, etc)
To add, IMO a circle should always be formed around a purpose (although you could propose one with just accountabilities), and "function" is just one of the grouping possibilities. Might just as well be "target group" or anything else.