It is possible to mark notifications as read in various ways through the API -- docs at https://developer.github.com/v3/activity/notifications/

However in the docs at http://pygithub.readthedocs.io/en/latest/github_objects/Notification.html I see nothing about how to mark a notification as read.

If mark-as-read functionality exists I would expect to find it in https://github.com/PyGithub/PyGithub/blob/master/github/Notification.py or maybe in https://github.com/PyGithub/PyGithub/blob/master/github/NotificationSubject.py but I don't see it.