I am a neuroscientist involved in some research which requires understanding how edge contractions affect the properties of graph-theoretic representations of large-scale networks. I have been looking through some resources on algebraic graph theory, however this topic seems to be a bit esoteric so I have not had much luck. If anyone can point me to some good resources on this I would be very grateful.
2025-01-12 23:35:51.1736724951
Resources on algebraic graph theory of edge contractions
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Edge contractions are not really so much algebraic graph theory as general graph theory. The subject is closely related to the subject of graph minors. Reinhard Diestel's book Graph Theory contains an entire chapter devoted to the famous graph minor theorem, including an outline of the proof. (The entire proof was published in a series of 20 papers.) The subject of edge contractions is very complicated, and there might not be many useful results for your research. In general, edge contractions tend to mess up most of the classic graph parameters.
If it turns out that the theory of graph minors is not what you're looking for, then I think you have to be a bit more specific. :-)