diff --git a/Data/Graph/Libgraph/Core.hs b/Data/Graph/Libgraph/Core.hs
--- a/Data/Graph/Libgraph/Core.hs
+++ b/Data/Graph/Libgraph/Core.hs
@@ -82,6 +82,10 @@
 --------------------------------------------------------------------------------
 -- Some other helper functions
 
+nothingIsFalse :: Maybe Bool -> Bool
+nothingIsFalse (Just b) = b
+nothingIsFalse Nothing  = False
+
 lookup' :: Eq a => a -> [(a, b)] -> String -> b
 lookup' x ys msg = case lookup x ys of
   Nothing -> error msg
diff --git a/Data/Graph/Libgraph/Cycles.hs b/Data/Graph/Libgraph/Cycles.hs
--- a/Data/Graph/Libgraph/Cycles.hs
+++ b/Data/Graph/Libgraph/Cycles.hs
@@ -84,9 +84,9 @@
 
 
 -- Part a and b of Havlak's algorithm
-state0 :: Ord vertex => Graph vertex arc -> CycleNest vertex
+state0 :: (Show vertex, Ord vertex) => Graph vertex arc -> CycleNest vertex
 state0 g = s0
-  where ps   = map (\w -> partition (isAncestor (dfs s0) w) (preds (graph s0) w)) [1..n s0]
+  where ps   = map (\w -> partition (isAncestor' (dfs s0) w) (preds (graph s0) w)) [1..n s0]
         bps  = map fst ps
         nbps = map snd ps
         dfsg = dfsGraph g
@@ -104,7 +104,11 @@
           , uf           = UF.fromList [1..n s0]
           }
 
-getCycleNest :: Ord vertex => Graph vertex arc -> CycleNest vertex
+isAncestor' d v w = case isAncestor d v w of 
+  Just b  -> b
+  Nothing -> error "Havlak's algorithm only works for connected graphs!"
+
+getCycleNest :: (Show vertex, Ord vertex) => Graph vertex arc -> CycleNest vertex
 getCycleNest g = execState (analyse . reverse $ [1..n s0]) s0
   where s0 = state0 g
 
@@ -164,7 +168,7 @@
   y' <- uf_find y
   d  <- gets dfs
   p  <- gets body
-  if not $ isAncestor d w y' then do
+  if not $ isAncestor' d w y' then do
     modifyVertexType (w,IrredHead)
     y' `addToNonBackPredsOf` w
   else if not (y' `elem` p) && y' /= w then do
@@ -175,11 +179,13 @@
 
 -- Some helper functions
 
-dfsGraph :: Ord vertex => Graph vertex arc -> (Graph Int (), Int -> vertex)
+dfsGraph :: (Show vertex, Ord vertex) => Graph vertex arc -> (Graph Int (), Int -> vertex)
 dfsGraph g = (mapGraph v2i g', i2v)
   where preorder = getPreorder (getDfs g)
-        i2v i = lookup' i (zip [1..] preorder) "Libraph.dfsGraph: lookup failed"
-        v2i v = lookup' v (zip preorder [1..]) "Libraph.dfsGraph: lookup failed"
+        i2v i = lookup' i (zip [1..] preorder) 
+              $ "Libraph.dfsGraph: unreachable from root " ++ show i
+        v2i v = lookup' v (zip preorder [1..])
+              $ "Libraph.dfsGraph: unreachable from root " ++ show v
         g' = unitGraph g
 
 modifyVertexType :: (Int,VertexType) -> S vertex ()
diff --git a/Data/Graph/Libgraph/Dagify.hs b/Data/Graph/Libgraph/Dagify.hs
--- a/Data/Graph/Libgraph/Dagify.hs
+++ b/Data/Graph/Libgraph/Dagify.hs
@@ -12,7 +12,7 @@
   where isBackEdge a = getEdgetype (getDfs g) a == BackEdge
         hasRedHead (Arc _ h _) = h `elem` getRedHeaders (getCycleNest g)
 
-collapse :: (Ord v,Eq a) => ([v]->v) -> Graph v a -> Graph v a
+collapse :: (Show v, Ord v,Eq a) => ([v]->v) -> Graph v a -> Graph v a
 collapse merge g = foldl collapseCycle g ics
   where (CycleTree _ ts) = getCycles (getCycleNest g)
         ics              = filter (\c -> case c of 
diff --git a/Data/Graph/Libgraph/DepthFirst.hs b/Data/Graph/Libgraph/DepthFirst.hs
--- a/Data/Graph/Libgraph/DepthFirst.hs
+++ b/Data/Graph/Libgraph/DepthFirst.hs
@@ -23,12 +23,14 @@
   deriving Eq
 
 -- | Is first vertex a (recursive) parent of second vertex?
+--   May fail when one of the vertices is unreachable from the root.
 isAncestor :: (Eq vertex, Show vertex)
-           => Dfs vertex arc -> vertex -> vertex -> Bool
-isAncestor d w v = (n_w <= n_v && n_v <= l_w)
-  where n_v    = lookup' v (num d) $ "LibGraph.isAncestor: lookup dfs number failed " ++ show v
-        n_w    = lookup' w (num d) $ "LibGraph.isAncestor: lookup dfs number failed"
-        l_w    = lookup' w (lastVisit d) $ "LibGraph.isAncestor: lookup dfs lasVisit-number failed"
+           => Dfs vertex arc -> vertex -> vertex -> Maybe Bool
+isAncestor d w v = do
+  n_v <- lookup v (num d)
+  n_w <- lookup w (num d)
+  l_w <- lookup w (lastVisit d)
+  return (n_w <= n_v && n_v <= l_w)
 
 -- | The 'EdgeType' of an 'Arc'.
 getEdgetype :: (Eq vertex, Show vertex) => Dfs vertex arc -> Arc vertex arc -> EdgeType
@@ -37,7 +39,7 @@
   | w `isAnc` v                 = BackEdge
   | v `isAnc` w                 = FwdEdge
   | otherwise                   = CrossEdge
-  where isAnc = isAncestor d
+  where isAnc x y = nothingIsFalse (isAncestor d x y)
 
 -- | Get list of vertices in the order they were visited by the depth-first search.
 getPreorder :: Dfs vertex arc -> [vertex]
@@ -114,7 +116,7 @@
 
 instance (Eq vertex,Show vertex) => Show (Dfs vertex arc) where
   show d = showWith (graph d) showVertex showArc
-    where showVertex v = show v ++ show (lkup v (num d), lkup v (lastVisit d))
+    where showVertex v = (show v ++ show (lkup v (num d), lkup v (lastVisit d)),"")
           showArc      = show . (getEdgetype d)
           lkup v ds    = lookup' v ds "Libgraph.show: lookup dfs number failed"
 
diff --git a/Data/Graph/Libgraph/Dominance.hs b/Data/Graph/Libgraph/Dominance.hs
--- a/Data/Graph/Libgraph/Dominance.hs
+++ b/Data/Graph/Libgraph/Dominance.hs
@@ -34,5 +34,5 @@
 
 instance (Eq vertex,Show vertex) => Show (Domsets vertex arc) where
   show d = showWith (graph d) showVertex showArc
-    where showVertex v = show v ++ show (getDominators v d)
+    where showVertex v = (show v ++ show (getDominators v d),"")
           showArc _    = ""
diff --git a/Data/Graph/Libgraph/Dot.hs b/Data/Graph/Libgraph/Dot.hs
--- a/Data/Graph/Libgraph/Dot.hs
+++ b/Data/Graph/Libgraph/Dot.hs
@@ -7,20 +7,26 @@
 import System.Process(runCommand)
 
 -- | Convert Graph to String with functions to show vertices and arcs.
-showWith :: Eq vertex => Graph vertex arc -> (vertex->String) -> (Arc vertex arc->String) -> String
+showWith :: Eq vertex => Graph vertex arc -> (vertex->(String,String)) 
+                          -> (Arc vertex arc->String) -> String
 showWith g vLabel aLabel
   = "diGraph G {\n"
-  ++ "root [style=invis label=\"\"]\n"
-  ++ foldl (\s v -> (showVertex vLabel v) ++ s) "" vs
-  ++ "root -> " ++ vName r ++ "\n"
+  ++ vName r ++ "[shape=none label=\".\"]\n"
+  ++ foldl (\s v -> show1 v ++ s) "" vs
   ++ foldl (\s a -> (showArc vs aLabel a) ++ s) "" (arcs g)
   ++ "}\n"
   where vs = zip (vertices g) [0..]
         r  = lookup' (root g) vs "LibGraph.showWith: lookup root in vs failed"
+        isRoot (v,_) = v == root g
 
-showVertex :: (vertex->String) -> (vertex,Int) -> String
-showVertex vLabel (v,i) 
-  = vName i ++ " [label=\"" ++ (escape . vLabel) v ++ "\"]\n"
+        show1 v
+          | isRoot v  = vName r ++ "[shape=none label=\".\"]\n"
+          | otherwise = (showVertex vLabel v)
+
+showVertex :: (vertex->(String,String)) -> (vertex,Int) -> String
+showVertex vLabel (v,i) =
+  let (lbl,extra) = vLabel v
+  in  vName i ++ " [label=\"" ++ escape lbl ++ "\"" ++ extra ++ "]\n"
 
 showArc :: Eq vertex => [(vertex,Int)] -> (Arc vertex arc->String) -> (Arc vertex arc) -> String
 showArc vs aLabel a
diff --git a/libgraph.cabal b/libgraph.cabal
--- a/libgraph.cabal
+++ b/libgraph.cabal
@@ -1,5 +1,5 @@
 Name:           libgraph
-Version:        1.3
+Version:        1.4
 Homepage:      http://maartenfaddegon.nl
 Synopsis:       Store and manipulate data in a graph.
 Description:    A graph type, analysis of graphs and manipulation of graphs.