node symmetric graph | vertex symmetric graph

A vertex-transitive graph, also sometimes called a node symmetric graph, is a graph such that every pair of vertices is equivalent under some element of its automorphism group. More explicitly, a vertex-transitive graph is a graph whose automorphism group is transitive. Informally speaking, a graph is vertex-transitive if every vertex has the same local environment, so that no vertex can be distinguished from any other based on the vertices and edges surrounding it. Another way of characterizing a vertex-transitive graph is as a graph for which the automorphism group has a single group orbit (i.e., the orbit lengths of its automorphism group are a single number).

arc-transitive graph | automorphism group | Cayley graph | cubic vertex-transitive graph | edge-transitive graph | Folkman graph | Gray graph | group orbit | nonhamiltonian graph | nonhamiltonian vertex-transitive graph | quartic vertex-transitive graph | semisymmetric graph | symmetric graph | transitive group