Bug introduced in 9.0.1 or earlier and fixed in 11.0.1

Consider the following two graphs:

g1 = Graph[{1, 2, 3}, {}];

g2 = SimpleGraph@Graph[{1, 2, 3}, {1 <-> 1}];

They are clearly the same thing because SimpleGraph will remove the self loop (only edge) from g2.

Yet IsomorphicGraphQ disagrees:

IsomorphicGraphQ[g1, g2]

(* False *)

I believe this is a bug and it exists in all of 9.0.1 through to 10.4.0.

Is there a workaround?

  • $\begingroup$ Given the example of Compress/Uncompress I agree that this is a bug and I added that tag accordingly. $\endgroup$
    – Mr.Wizard
    Commented Jul 19, 2015 at 10:55
  • $\begingroup$ @Mr.Wizard, given your geo, any chance you can be in Pasadena early Aug for a day? ... Szabolcs, I'd extend the same invite but you're a bit further @ away this time. $\endgroup$ Commented Jul 19, 2015 at 12:30
  • 1
    $\begingroup$ @alancalvitti I don't think that will be possible but I must say I am curious why you ask. $\endgroup$
    – Mr.Wizard
    Commented Jul 19, 2015 at 12:53
  • $\begingroup$ @Mr.Wizard, you already know why: software is eating the world and M.SE is a global lever. Take a look at some of the tech in this useful fiction like Ghost Fleet >> bit.ly/1e7MJ38. If you like it I'll msg you a 2-part key w/ info. $\endgroup$ Commented Jul 20, 2015 at 17:15
  • $\begingroup$ @alancalvitti is this poetry? $\endgroup$
    – shrx
    Commented Oct 16, 2015 at 12:13

1 Answer 1


A simple workaround is to re-build the graph object by cycling it through some other representation. Here are two possible solutions:

rebuildGraph[g_] := Uncompress@Compress[g] (* solution 1 *)
rebuildGraph[g_] := Graph[VertexList[g], EdgeList[g]] (* solution 2 destroys properties but it's fine for isomorphism testing purposes *)

isomorphicGraphQ[g1_, g2_] := 
 IsomorphicGraphQ[rebuildGraph[g1], rebuildGraph[g2]]

Now this gives a correct result:

isomorphicGraphQ[g1, g2]
(* True *)

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