Conceptual question on serializing data with circular references

I am trying to implement a serializer in python which tries to do something like this.

If there is an object Foo, having a forward reference to Bar, the serializer would dump all the data in Foo, and the reference would be converted into a data dump of Bar. Things would be done recursively like this for any arbitrary depth.

But there is a problem I run into with this approach, that of circular references, what if Foo references Bar and Bar references Foo? An infinite recursion would be created then.

What are the approaches to tackling this problem.

Note: I have no control over the data I would be serializing, so I can't rule out circular references.

Flatten out the structure beforehand with a depth-first search that records which items it has seen. Assign each object an id and replace object references with id references.

(In essence, turn it into a graph.)

Keep a list of objects you've already serialized. Every object you attempt to serialize should be checked against this list. A similar approach is to toggle a boolean within each object as to whether it's been serialized already, and thus not to continue for this object.

Study the Python pickle module which automatically handles circular references through serialization. It uses object ids to store references. Source code for Python 2.6.6 is here.