Graphs and C-sets III: Reflexive graphs and C-set homomorphisms

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Continuing our tour of the many flavors of graphs and their manifestation as -sets, we discuss reflexive graphs, a seemingly minor variant of graphs that nonetheless has some interesting and distinctive features. A reflexive graph is a graph where every vertex has a distinguished self-loop, like this:


This is a companion discussion topic for the original entry at https://blog.algebraicjulia.org/post/2021/04/cset-graphs-3/