ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 01 Aug 2019 04:21:31 -0500Automorphism group of edge symmetryhttp://ask.sagemath.org/question/47334/automorphism-group-of-edge-symmetry/ I asked a similar question before,
https://ask.sagemath.org/question/42762/automorphism-group-of-weighted-graph/
I am curious that is there any similar function for finding "edge symmetry"?
Note: the link I provided is for "node symmetry" in a network (graph). sleeve chenThu, 01 Aug 2019 04:21:31 -0500http://ask.sagemath.org/question/47334/Automorphism group of weighted graphhttp://ask.sagemath.org/question/42762/automorphism-group-of-weighted-graph/I know we can use sage to find the group of automorphisms of a graph $G$:
G.automorphism_group().list()
However, the above way can only be used to the unweighted graph. So for example:
G = matrix([[0,10,0],
[10,0,1],
[0,1,0]])
G1 = Graph(G, weighted = True)
G1.show(edge_labels=True )
G.automorphism_group().list()
The result is:
[(), (0,2)]
However, this result is not correct (correct for unweighted case). This is because $AD\neq DA$, where
$$D = \begin{bmatrix} 0 & 0 & 1 \\\ 0 & 1 & 0 \\\ 1 & 0 & 0\end{bmatrix},$$ which is a permutation matrix and
$$A = \begin{bmatrix} 0 & 10 & 0 \\\ 10 & 0 & 1 \\\ 0 & 1 & 0\end{bmatrix},$$ which is an adjacency matrix.
Can we use SAGE to find the group of automorphisms of a graph?sleeve chenWed, 27 Jun 2018 20:22:14 -0500http://ask.sagemath.org/question/42762/