Random Graphs
The proportion of graphs on n vertices with nontrivial automorphism tends to zero as n grows, which is informally expressed as "almost all finite graphs are asymmetric". In contrast, again informally, "almost all infinite graphs are symmetric." More specifically, countable infinite random graphs in the Erdős–Rényi model are, with probability 1, isomorphic to the highly symmetric Rado graph.
Read more about this topic: Asymmetric Graph
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