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