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How to find all simple cycles in an undirected graph efficiently?

Given a graph, what are some of the best algorithms (what is the best algorithm) to find all the simple paths (i.e. no cycles) between any two nodes?

  • Some of the edges are undirected, some of them are directed.. That being the case, what is the best algorithm to find all the simple paths in a graph?

  • Answer:

    Breadth First Search should work(Make the BFS tree and you will get all simple paths).Regarding the huge number of paths, there can be O(2^|V|) paths and you need to know all those paths, so any algorithm will go for a toss.

Ambar Pal at Quora Visit the source

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The National Institute of Standards and Technology (NIST) online Dictionary of Algorithms and Data Structures describes this particular problem as http://xlinux.nist.gov/dads//HTML/allSimplePaths.html and recommends a http://xlinux.nist.gov/dads//HTML/depthfirst.html to find all non-cyclical paths between arbitrary pairs of nodes.

Andrew Webb

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