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I have the following code which gives me some random complete graph

rand = {1, 2, 3};
el = EdgeList[CompleteGraph[5]];
g = CompleteGraph[5, VertexLabels -> "Name", 
  EdgeLabels -> Table[el[[i]] -> RandomChoice[rand], {i, Length[el]}]]

What I want is to get every possible graph with edges labeled with numbers from rand.

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  • $\begingroup$ I wanna get every graph in some sort of cycle like For because every iteration I should do something with the graph I've got. $\endgroup$
    – mclord
    Commented Dec 22, 2021 at 19:01
  • $\begingroup$ Are you sure you need all those labeled graphs? Look at the result of Tuples[{1, 2, 3}, 10], for instance. $\endgroup$ Commented Dec 22, 2021 at 19:03
  • $\begingroup$ I'm pretty sure I need all of them since I should counts paths in all this graphs. $\endgroup$
    – mclord
    Commented Dec 22, 2021 at 19:11
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    $\begingroup$ To make the hint in my previous comment more explicit: there are $59049$ of those labeled graphs. If you absolutely must, this question might be of interest. $\endgroup$ Commented Dec 22, 2021 at 19:17
  • $\begingroup$ I feel like we have 3 possibilities for each edge, and are there 3^(10*9/2) (=2954312706550833698643) of those labeled graphs? Of course, a lot of these graphs are isomorphic, and we have to figure out how to get rid of them. $\endgroup$
    – licheng
    Commented Dec 23, 2021 at 2:27

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