They are pretty darn rare. Also they can be aggressive. I saw one chase my friend years ago (36 yrs ago), it was friggin hilarious, we didn't see him (my friend) for half an hour.
It was funny because he was trying to get me and his brother to jump this creek, and the Swan was patrolling, we could tell it was getting defensive. He mocked us and jumped and the Swan went full on at him, did I mention we just smoked a joint ? His brother was on his knees he was laughing so hard. Swan's necks are pretty big, and I would not want to get bit by one. We think they are soft and fluffy because of the toilet paper.