I want to generate all the possible adjacency matrices of equivalent unlabeled graphs. For example, consider the simple path graph of three vertices. There are three possible adjacency matrices:

a1={{0, 1, 0}, {1, 0, 1}, {0, 1, 0}};
a2={{0, 1, 1}, {1, 0, 0}, {1, 0, 0}};
a3={{0, 0, 1}, {0, 0, 1}, {1, 1, 0}};

Each matrix corresponding to a different (numerical) labeling of the vertices.

Is there a way to generate the other representations given any one of them for any simply connected graph?

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