Finding all cycles in an undirected graph

[Fabian]

Dear networkx-discuss,

I searched for this problem within this group for a while but couldn't find a satisfying solution.

Given an undirected graph G, how can I find all cycles in G?
I believe that I should use cycle_basis. The documentation says

A basis for cycles of a network is a minimal collection of cycles such that any cycle in the network can be written as a sum of cycles in the basis. Here summation of cycles is defined as “exclusive or” of the edges.

How can I enumerate all sums of cycles in the basis and hence enumerate all cycles?
I would like to use as much from the networkx package as possible, and hopefully there is an easy way.

Thank you for your help!
-Fabian

[Daniel Schult]

Maybe you can explain why you want to do such a thing. Do you mean all simple cycles? (There's a stackoverflow question about that and a NetworkX function to provide it  

To show the issue with the question, let's say that you have two cycles called a and b in the basis. Then other cycles can be ab, aa, aba, abba, baba, ..., babababababbbbababbbabababababb... :}   without any restriction you can keep going around a as long as you want before passing to b and going around that cycle.

I think a cycle_basis is enough for most questions and simple_cycles should fill in most others. Does this help?

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[Fabian]

Sorry, yes, I mean all simple cycles.
The reason I dismissed simple_cycles was that it is defined for directed graphs.
But I could just use

G=nx.Graph()
#...
H=G.to_directed()
simple_cycles=list(nx.simple_cycles(H))

Correct? Thanks for your help!

[Daniel Schult]

On Tue, Jan 26, 2016 at 3:39 AM, Fabian <fabian.r...@gmail.com> wrote:

Sorry, yes, I mean all simple cycles.
The reason I dismissed simple_cycles was that it is defined for directed graphs.
But I could just use

G=nx.Graph()
#...
H=G.to_directed()
simple_cycles=list(nx.simple_cycles(H))

Correct? Thanks for your help!

Yes -- The G.to_directed() replaces each undirected edge with two directed edges. You can manually create other replacements, but I think this is what you probably want. :)