Strange Python set and hash behaviour - how does this work?

I have a class called `GraphEdge` which I would like to be uniquely defined within a set (the built-in `set` type) by its `tail` and `head` members, which are set via `__init__`. If I do not define `__hash__`, I see the following behaviour: ``` >>> E = GraphEdge('A', 'B') >>> H = GraphEdge('A', 'B') >>> hash(E) 139731804758160 >>> hash(H) 139731804760784 >>> S = set() >>> S.add(E) >>> S.add(H) >>> S set([('A', 'B'), ('A', 'B')]) ``` The set has no way to know that `E` and `H` are the same by my definition, since they have differing hashes (which is what the set type uses to determine uniqueness, to my knowledge), so it adds both as distinct elements. So I define a rather naive hash function for `GraphEdge` like so: ``` def __hash__( self ): return hash( self.tail ) ^ hash( self.head ) ``` Now the above works as expected: ``` >>> E = GraphEdge('A', 'B') >>> H = GraphEdge('A', 'B') >>> hash(E) 409150083 >>> hash(H) 409150083 >>> S = set() >>> S.add(E) >>> S.add(H) >>> S set([('A', 'B')]) ``` But clearly, `('A', 'B')` and `('B', 'A')` in this case will return the same hash, so I would expect that I could not add `('B', 'A')` to a set already containing `('A', 'B')`. But this is not what happens: ``` >>> E = GraphEdge('A', 'B') >>> H = GraphEdge('B', 'A') >>> hash(E) 409150083 >>> hash(H) 409150083 >>> S = set() >>> S.add(E) >>> S.add(H) >>> S set([('A', 'B'), ('B', 'A')]) ``` So is the set type using the hash or not? If so, how is the last scenario possible? If not, why doesn't the first scenario (no `__hash__` defined) work? Am I missing something? Edit: For reference for future readers, I already had `__eq__` defined (also based on `tail` and `head`).