How to detect cycles when using shared_ptr

shared_ptr is a reference counting smart pointer in the Boost library.

The problem with reference counting is that it cannot dispose of cycles. I am wondering how one would go about solving this in C++.

Please no suggestions like: "don't make cycles", or "use weak_ptr".

Edit

I don't like suggestions that say to just use a weak_ptr because obviously if you know you will create a cycle, then you wouldn't have a problem. You also cannot know you will have a cycle at compile time if you generate shared_ptrs at runtime.

So please, self delete answers that use weak_ptr in them because I specifically asked not to have those kind of answers...