Your example still fits with my (tentative) definition. For both circles, it is true that each member has exactly two friendship relations in it. My definition does not say anything about the number of overall friendship relations on the whole site, but only about friendship relations within a circle.

But I think I need a second thing in the definition, but I'm not sure which one is "better":

• A "circle of friends" must have at least three members
• There must be at least one person for every member of the circle without a direct "friend" relation

The two are not equivalent, because the first rule allows circles of three persons, while the latter allows circles starting at four members.