Jon Peltier has written about graphs based on hours of the day (and chosen the perfect title, so I have to make do with second best), with examples attempting to show the day and night cycles together intuitively.
I think the whole day-night split thing is artificial: there's no connection between the times that are twelve hours apart and happen to have the same number under our old mediæval twelve hour day, twelve hour night scheme. I'm surprised how much less Americans use the 24 hour clock, and how they call it "military time" when they do. In Britain we associate it more with the coming of the railways in the nineteenth century, and the need for standard timetables (until trains made national time zones necessary, individual towns had their own time!) I've made a polar area graph on a 24 hour scheme here:
The polar area graph is one of my favourite neglected specialist graph types, but it really only has a chance of being the graph type of choice if
a) you don't mind reading stacked areas instead of position along a common scale (see Cleveland's Hierarchy),
b) the data set is truly cyclic, not linear, and
c) there are two series to compare, one much smaller than the other (here we lack a second, smaller series that could be plotted closer to the centre, to take advantage of the square root relationship between the area of the slices and their radius)
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