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Finding number and list of automorphisms given adjacency matrix

Posted 11 years ago
This is probably a silly question, but I can't find an answer.

I have various adjacency matrices and I want to 1) draw graphs of them, 2) determine the number of automorphisms of the graph, and 3) determine the automorphisms of the graph.

I can do 1)

Here is my code:

x = AdjacencyGraph[ *(adjacency matrix goes here)* ]
Automorphisms[x] //TraditionalForm

Line 2 does what I want it to do, but line 3 and 4 don't do what I want them to do.

Can anybody help me?

Thank you in advance.
POSTED BY: Raheman Velji
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Posted 11 years ago
found an answer in another thread:

line 4 should read:

Automorphisms[FromAdjacencyMatrix] // TraditionalForm
where y is a matrix

still can't get line 3 to work.
POSTED BY: Raheman Velji

In Mathematica 10, we can do:

  • AdjacencyGraph[mat] to get the graph
  • GroupOrder@GraphAutomorphismGroup@AdjacencyGraph[mat] to find the number of automorphisms without listing each of them (which would be slow).

With IGraph/M, you can also use

  • IGBlissAutomorphismCount@AdjacencyGraph[mat] to count automorphisms very fast.
POSTED BY: Szabolcs Horvát
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