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How do you call a graph where all the nodes are equivalent in the sense that each node sees the same graph structure from its own perspective? "isotropic", maybe?
Examples:
- a polygon
- an infinite grid
- a complete graph
- a toroidal grid
- n nodes 0 ... n-1 such that each node i is connected to nodes { (i+offs) mod n | offs in offsets }, given a list of offsets i.e. a subset of [1, n-1]
"vertex-transitive" is what I was looking for. Woohoo. https://en.wikipedia.org/wiki/Vertex-transitive_graph
If I understand what a graph automorphism is, what I want is a name for the graphs that satisfy:
For each vertex pair (u, v) there is an automorphism f such that f(u) = v.
A symmetric graph is not exactly that, and I'm a bit confused. https://en.wikipedia.org/wiki/Symmetric_graph