Redo/refactor calculations and caching of properties such as degrees

[eriknw]

We compute and cache many properties such as has_self_edges, degrees- (w/o diagonals), degrees+ (with diagonals), etc., which is actually very handy. However, the code is a little complicated (cough cough, my bad) and may be error prone (see: #82 (comment)). It would be great if we could refactor this to be more clear, maintainable, and safe. I imagine such a solution would be more declarative and less procedural.