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(***) Conversions

Write predicates to convert between the different graph representations.

Here is a working solution for the graph-term, adjacency-list, and edge-clause / human-friendly forms for undirected, unweighted graphs.

data Graph a = Graph [a] [(a, a)]
               deriving (Show, Eq)
 
data Adjacency a = Adj [(a, [a])]
		   deriving (Show, Eq)
 
data Friendly a = Edge [(a, a)]
		  deriving (Show, Eq)
 
graphToAdj :: (Eq a) => Graph a -> Adjacency a
graphToAdj (Graph [] _)	     = Adj []
graphToAdj (Graph (x:xs) ys) = Adj ((x, ys >>= f) : zs)
   where 
      f (a, b) 
         | a == x = [b]
         | b == x = [a]
         | otherwise = []
      Adj zs = graphToAdj (Graph xs ys)
 
adjToGraph :: (Eq a) => Adjacency a -> Graph a
adjToGraph (Adj [])          = Graph [] []
adjToGraph (Adj ((v, a):vs)) = Graph (v : xs) ((a >>= f) ++ ys)
   where
      f x = if (v, x) `elem` ys || (x, v) `elem` ys
            then []
            else [(v, x)]
      Graph xs ys = adjToGraph (Adj vs)
 
graphToFri :: (Eq a) => Graph a -> Friendly a
graphToFri (Graph [] _)  = Edge []
graphToFri (Graph xs ys) = Edge (ys ++ zip g g)
   where
      g = filter (\x -> all (\(a, b) -> x /= a && x /= b) ys) xs
 
friToGraph :: (Eq a) => Friendly a -> Graph a
friToGraph (Edge []) = Graph [] []
friToGraph (Edge vs) = Graph xs ys
   where
      xs = foldr acc [] $ concat $ map (\(a, b) -> [a, b]) vs
      ys = filter (uncurry (/=)) vs
      acc x xs = if x `elem` xs then xs else x : xs
 
adjToFri :: (Eq a) => Adjacency a -> Friendly a
adjToFri = graphToFri . adjToGraph
 
friToAdj :: (Eq a) => Friendly a -> Adjacency a
friToAdj = graphToAdj . friToGraph