# How can I count the number of cycles of special length in a graph in sage?

I have tried the G.subgraph_search_count(graphs.CycleGraph(4))but it doesn't lead to the correct answer, any help would be appreciated.

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Would it suffice to divide by the size of the automorphism group of the subgraph that is being searched for, perhaps? In other words, are you trying to count non labelled occurrences of cycles? For the particular case stated in your question, dividing by 8 might do the trick.

( 2016-12-02 17:00:46 +0200 )edit

Yes ,That's what I'm trying to do,but what is 8 that it should be divided by?

( 2016-12-02 20:10:26 +0200 )edit

I meant you should divide by 8 if you are searching 4-cycles, since the size of the automorphism group of the 4-cycle is 8. See answer below for further details.

( 2016-12-03 17:49:39 +0200 )edit

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Seems like you are searching for non labelled occurrences of cycles. In such case dividing by the size of the automorphism group of the graph that is being searched for might do the trick. Say you are trying to count the number of unlabelled appearances of graph H in graph G. You can define

subgraph_count = lambda G,H: G.subgraph_search_cound(H)/H.automorphism_group(return_group=False,order=True)


and then use

G=graphs.Grid2dGraph(3,3)
H=graphs.CycleGraph(4)
subgraph_count(G,H)


This should output 4, as expected.

For the particular case of cycles, if you are searching for cycles of length k then it suffices to divide by 2*k, so the following should work.

cycle_subgraph_count = lambda G,k: G.subgraph_search_cound(graphs.CycleGraph(k))/(2*k)


then

G=graphs.Grid2dGraph(10,10)
cycle_subgraph_count(G,4)


should output 81.

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Thank you so much,I got it.

( 2016-12-03 19:32:40 +0200 )edit

You're welcome! If this worked for you, you can mark the answer as accepted ;-)

( 2016-12-03 20:15:29 +0200 )edit