Getting all possible graphs

Asked Dec 22 '21 at 19:00

Active Dec 22 '21 at 19:00

Viewed 74 times

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.

asked Dec 22 '21 at 19:00

mclord

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. – mclord Dec 22 '21 at 19:01
Are you sure you need all those labeled graphs? Look at the result of Tuples[{1, 2, 3}, 10], for instance. – J. M.'s missing motivation Dec 22 '21 at 19:03
I'm pretty sure I need all of them since I should counts paths in all this graphs. – mclord Dec 22 '21 at 19:11
2

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. – J. M.'s missing motivation Dec 22 '21 at 19:17
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. – licheng Dec 23 '21 at 02:27
Sorry, I made a mistake and thought it was 10 vertices. – licheng Dec 23 '21 at 02:32
@li, an $n$-vertex complete graph has $\dbinom{n}{2}$ edges, which makes for $k^{\binom{n}{2}}$ total labelings for $k$ possible edge labels. – J. M.'s missing motivation Dec 23 '21 at 08:22

Getting all possible graphs

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