Graph automorphism is a concept in graph theory that refers to a symmetry of a graph that preserves its structure. More specifically, an automorphism of a graph is a bijection (one-to-one and onto mapping) from the set of vertices of the graph to itself that preserves the adjacency relationship between vertices.
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A graph automorphism is a bijection of the vertex set that preserves adjacency. It preserves graph distances and transports simple random-walk hitting problems between vertices.