loops

simpleLoops :: Graph -> [Path]
simpleLoops g = filterUniqueCycles $ concatMap (simpleLoopsFrom g) (map (:[]) $ vertices g)

simpleLoopsFrom :: Graph -> Path -> [Path]
simpleLoopsFrom g p
    | isSimpleLoop p  = [p]
    | otherwise = concatMap (simpleLoopsFrom g) (map (:p) ov)
        where
            first = head p
            ov = filter (not . (`elem` (init p))) $ outVertices g first

isSimpleLoop :: Path -> Bool
isSimpleLoop p = length p > 1 && head p == last p

filterUniqueCycles :: [Path] -> [Path]
filterUniqueCycles = (flip foldr []) $ \p ac ->
    let cycles = map (concat . replicate 2 . tail) ac :: [Path]
    in if any (p `isInfixOf`) cycles then ac
                                     else p:ac