More specifically, why should the hourly average visit duration graph look like this:
It's as if there's some sort of daily artefact in the data or method of calculation. This pattern doesn't appear in any other graphs.
Google-analytics – How does Google Analytics calculate average visit duration
google analytics
Best Answer
https://support.google.com/analytics/answer/1006253?hl=en explains how they compute the average visit duration: in short the formula is
(The time of the first hit on the last page - the first hit on the first page) / (number of visited pages).Regarding your second question pertaining to your graph, try https://stackoverflow.com/q/15841370/395857