    {-# LANGUAGE CPP #-}

    -- (c) 1999-2005 by Martin Erwig [see file COPYRIGHT]
    -- | Static and Dynamic Inductive Graphs
    module Data.Graph.Inductive.Graph (
        -- * General Type Defintions
        -- ** Node and Edge Types
        Node,LNode,UNode,
        Edge,LEdge,UEdge,
        -- ** Types Supporting Inductive Graph View
        Adj,Context,MContext,Decomp,GDecomp,UContext,UDecomp,
        Path,LPath(..),UPath,
        -- * Graph Type Classes
        -- | We define two graph classes:
        --
        --   Graph: static, decomposable graphs.
        --    Static means that a graph itself cannot be changed
        --
        --   DynGraph: dynamic, extensible graphs.
        --             Dynamic graphs inherit all operations from static graphs
        --             but also offer operations to extend and change graphs.
        --
        -- Each class contains in addition to its essential operations those
        -- derived operations that might be overwritten by a more efficient
        -- implementation in an instance definition.
        --
        -- Note that labNodes is essentially needed because the default definition
        -- for matchAny is based on it: we need some node from the graph to define
        -- matchAny in terms of match. Alternatively, we could have made matchAny
        -- essential and have labNodes defined in terms of ufold and matchAny.
        -- However, in general, labNodes seems to be (at least) as easy to define
        -- as matchAny. We have chosen labNodes instead of the function nodes since
        -- nodes can be easily derived from labNodes, but not vice versa.
        Graph(..),
        DynGraph(..),
        -- * Operations
        order,
        size,
        -- ** Graph Folds and Maps
        ufold,gmap,nmap,emap,nemap,
        -- ** Graph Projection
        nodes,edges,toEdge,edgeLabel,toLEdge,newNodes,gelem,
        -- ** Graph Construction and Destruction
        insNode,insEdge,delNode,delEdge,delLEdge,delAllLEdge,
        insNodes,insEdges,delNodes,delEdges,
        buildGr,mkUGraph,
        -- ** Subgraphs
        gfiltermap,nfilter,labnfilter,labfilter,subgraph,
        -- ** Graph Inspection
        context,lab,neighbors,lneighbors,
        suc,pre,lsuc,lpre,
        out,inn,outdeg,indeg,deg,
        hasEdge,hasNeighbor,hasLEdge,hasNeighborAdj,
        equal,
        -- ** Context Inspection
        node',lab',labNode',neighbors',lneighbors',
        suc',pre',lpre',lsuc',
        out',inn',outdeg',indeg',deg',
        -- * Pretty-printing
        prettify,
        prettyPrint,
        -- * Ordering of Graphs
        OrdGr(..)
    ) where

    import           Control.Arrow (first)
    import           Data.Function (on)
    import qualified Data.IntSet   as IntSet
    import           Data.List     (delete, foldl', groupBy, sort, sortBy, (\\))
    import           Data.Maybe    (fromMaybe, isJust)

    #if __GLASGOW_HASKELL__ < 710
    import Data.Monoid (mappend)
    #endif

    -- | Unlabeled node
    type  Node   = Int
    -- | Labeled node
    type LNode a = (Node,a)
    -- | Quasi-unlabeled node
    type UNode   = LNode ()

    -- | Unlabeled edge
    type  Edge   = (Node,Node)
    -- | Labeled edge
    type LEdge b = (Node,Node,b)
    -- | Quasi-unlabeled edge
    type UEdge   = LEdge ()

    -- | Unlabeled path
    type Path    = [Node]
    -- | Labeled path
    newtype LPath a = LP { unLPath :: [LNode a] }

    instance (Show a) => Show (LPath a) where
      show (LP xs) = show xs

    instance (Eq a) => Eq (LPath a) where
      (LP [])        == (LP [])        = True
      (LP ((_,x):_)) == (LP ((_,y):_)) = x==y
      (LP _)         == (LP _)         = False

    instance (Ord a) => Ord (LPath a) where
      compare (LP [])        (LP [])        = EQ
      compare (LP ((_,x):_)) (LP ((_,y):_)) = compare x y
      compare _ _ = error "LPath: cannot compare two empty paths"

    -- | Quasi-unlabeled path
    type UPath   = [UNode]

    -- | Labeled links to or from a 'Node'.
    type Adj b        = [(b,Node)]
    -- | Links to the 'Node', the 'Node' itself, a label, links from the 'Node'.
    --
    --   In other words, this captures all information regarding the
    --   specified 'Node' within a graph.
    type Context a b  = (Adj b,Node,a,Adj b) -- Context a b "=" Context' a b "+" Node
    type MContext a b = Maybe (Context a b)
    -- | 'Graph' decomposition - the context removed from a 'Graph', and the rest
    -- of the 'Graph'.
    type Decomp g a b = (MContext a b,g a b)
    -- | The same as 'Decomp', only more sure of itself.
    type GDecomp g a b  = (Context a b,g a b)

    -- | Unlabeled context.
    type UContext     = ([Node],Node,[Node])
    -- | Unlabeled decomposition.
    type UDecomp g    = (Maybe UContext,g)

    -- | Minimum implementation: 'empty', 'isEmpty', 'match', 'mkGraph', 'labNodes'
    class Graph gr where
      {-# MINIMAL empty, isEmpty, match, mkGraph, labNodes #-}

      -- | An empty 'Graph'.
      empty     :: gr a b

      -- | True if the given 'Graph' is empty.
      isEmpty   :: gr a b -> Bool

      -- | Decompose a 'Graph' into the 'MContext' found for the given node and the
      -- remaining 'Graph'.
      match     :: Node -> gr a b -> Decomp gr a b

      -- | Create a 'Graph' from the list of 'LNode's and 'LEdge's.
      --
      --   For graphs that are also instances of 'DynGraph', @mkGraph ns
      --   es@ should be equivalent to @('insEdges' es . 'insNodes' ns)
      --   'empty'@.
      mkGraph   :: [LNode a] -> [LEdge b] -> gr a b

      -- | A list of all 'LNode's in the 'Graph'.
      labNodes  :: gr a b -> [LNode a]

      -- | Decompose a graph into the 'Context' for an arbitrarily-chosen 'Node'
      -- and the remaining 'Graph'.
      matchAny  :: gr a b -> GDecomp gr a b
      matchAny g = case labNodes g of
                     []      -> error "Match Exception, Empty Graph"
                     (v,_):_ -> (c,g')
                       where
                         (Just c,g') = match v g

      -- | The number of 'Node's in a 'Graph'.
      noNodes   :: gr a b -> Int
      noNodes = length . labNodes

      -- | The minimum and maximum 'Node' in a 'Graph'.
      nodeRange :: gr a b -> (Node,Node)
      nodeRange g
        | isEmpty g = error "nodeRange of empty graph"
        | otherwise = (minimum vs, maximum vs)
        where
          vs = nodes g

      -- | A list of all 'LEdge's in the 'Graph'.
      labEdges  :: gr a b -> [LEdge b]
      labEdges = ufold (\(_,v,_,s)->(map (\(l,w)->(v,w,l)) s ++)) []

    class (Graph gr) => DynGraph gr where
      -- | Merge the 'Context' into the 'DynGraph'.
      --
      --   Context adjacencies should only refer to either a Node already
      --   in a graph or the node in the Context itself (for loops).
      --
      --   Behaviour is undefined if the specified 'Node' already exists
      --   in the graph.
      (&) :: Context a b -> gr a b -> gr a b

    -- | The number of nodes in the graph.  An alias for 'noNodes'.
    order :: (Graph gr) => gr a b -> Int
    order = noNodes

    -- | The number of edges in the graph.
    --
    --   Note that this counts every edge found, so if you are
    --   representing an unordered graph by having each edge mirrored this
    --   will be incorrect.
    --
    --   If you created an unordered graph by either mirroring every edge
    --   (including loops!) or using the @undir@ function in
    --   "Data.Graph.Inductive.Basic" then you can safely halve the value
    --   returned by this.
    size :: (Graph gr) => gr a b -> Int
    size = length . labEdges

    -- | Fold a function over the graph by recursively calling 'match'.
    ufold :: (Graph gr) => (Context a b -> c -> c) -> c -> gr a b -> c
    ufold f u g
      | isEmpty g = u
      | otherwise = f c (ufold f u g')
      where
        (c,g') = matchAny g

    -- | Map a function over the graph by recursively calling 'match'.
    gmap :: (DynGraph gr) => (Context a b -> Context c d) -> gr a b -> gr c d
    gmap f = ufold (\c->(f c&)) empty
    {-# NOINLINE [0] gmap #-}

    -- | Map a function over the 'Node' labels in a graph.
    nmap :: (DynGraph gr) => (a -> c) -> gr a b -> gr c b
    nmap f = gmap (\(p,v,l,s)->(p,v,f l,s))
    {-# NOINLINE [0] nmap #-}

    -- | Map a function over the 'Edge' labels in a graph.
    emap :: (DynGraph gr) => (b -> c) -> gr a b -> gr a c
    emap f = gmap (\(p,v,l,s)->(map1 f p,v,l,map1 f s))
      where
        map1 g = map (first g)
    {-# NOINLINE [0] emap #-}

    -- | Map functions over both the 'Node' and 'Edge' labels in a graph.
    nemap :: (DynGraph gr) => (a -> c) -> (b -> d) -> gr a b -> gr c d
    nemap fn fe = gmap (\(p,v,l,s) -> (fe' p,v,fn l,fe' s))
      where
        fe' = map (first fe)
    {-# NOINLINE [0] nemap #-}

    -- | List all 'Node's in the 'Graph'.
    nodes :: (Graph gr) => gr a b -> [Node]
    nodes = map fst . labNodes

    -- | List all 'Edge's in the 'Graph'.
    edges :: (Graph gr) => gr a b -> [Edge]
    edges = map toEdge . labEdges

    -- | Drop the label component of an edge.
    toEdge :: LEdge b -> Edge
    toEdge (v,w,_) = (v,w)

    -- | Add a label to an edge.
    toLEdge :: Edge -> b -> LEdge b
    toLEdge (v,w) l = (v,w,l)

    -- | The label in an edge.
    edgeLabel :: LEdge b -> b
    edgeLabel (_,_,l) = l

    -- | List N available 'Node's, i.e. 'Node's that are not used in the 'Graph'.
    newNodes :: (Graph gr) => Int -> gr a b -> [Node]
    newNodes i g
      | isEmpty g = [0..i-1]
      | otherwise = [n+1..n+i]
      where
        (_,n) = nodeRange g

    -- | 'True' if the 'Node' is present in the 'Graph'.
    gelem :: (Graph gr) => Node -> gr a b -> Bool
    gelem v = isJust . fst . match v

    -- | Insert a 'LNode' into the 'Graph'.
    insNode :: (DynGraph gr) => LNode a -> gr a b -> gr a b
    insNode (v,l) = (([],v,l,[])&)
    {-# NOINLINE [0] insNode #-}

    -- | Insert a 'LEdge' into the 'Graph'.
    insEdge :: (DynGraph gr) => LEdge b -> gr a b -> gr a b
    insEdge (v,w,l) g = (pr,v,la,(l,w):su) & g'
      where
        (mcxt,g') = match v g
        (pr,_,la,su) = fromMaybe
                         (error ("insEdge: cannot add edge from non-existent vertex " ++ show v))
                         mcxt
    {-# NOINLINE [0] insEdge #-}

    -- | Remove a 'Node' from the 'Graph'.
    delNode :: (Graph gr) => Node -> gr a b -> gr a b
    delNode v = delNodes [v]

    -- | Remove an 'Edge' from the 'Graph'.
    --
    --   NOTE: in the case of multiple edges, this will delete /all/ such
    --   edges from the graph as there is no way to distinguish between
    --   them.  If you need to delete only a single such edge, please use
    --   'delLEdge'.
    delEdge :: (DynGraph gr) => Edge -> gr a b -> gr a b
    delEdge (v,w) g = case match v g of
                        (Nothing,_)          -> g
                        (Just (p,v',l,s),g') -> (p,v',l,filter ((/=w).snd) s) & g'

    -- | Remove an 'LEdge' from the 'Graph'.
    --
    --   NOTE: in the case of multiple edges with the same label, this
    --   will only delete the /first/ such edge.  To delete all such
    --   edges, please use 'delAllLedge'.
    delLEdge :: (DynGraph gr, Eq b) => LEdge b -> gr a b -> gr a b
    delLEdge = delLEdgeBy delete

    -- | Remove all edges equal to the one specified.
    delAllLEdge :: (DynGraph gr, Eq b) => LEdge b -> gr a b -> gr a b
    delAllLEdge = delLEdgeBy (filter . (/=))

    delLEdgeBy :: (DynGraph gr) => ((b,Node) -> Adj b -> Adj b)
                  -> LEdge b -> gr a b -> gr a b
    delLEdgeBy f (v,w,b) g = case match v g of
                               (Nothing,_)          -> g
                               (Just (p,v',l,s),g') -> (p,v',l,f (b,w) s) & g'

    -- | Insert multiple 'LNode's into the 'Graph'.
    insNodes   :: (DynGraph gr) => [LNode a] -> gr a b -> gr a b
    insNodes vs g = foldl' (flip insNode) g vs
    {-# INLINABLE insNodes #-}

    -- | Insert multiple 'LEdge's into the 'Graph'.
    insEdges :: (DynGraph gr) => [LEdge b] -> gr a b -> gr a b
    insEdges es g = foldl' (flip insEdge) g es
    {-# INLINABLE insEdges #-}

    -- | Remove multiple 'Node's from the 'Graph'.
    delNodes :: (Graph gr) => [Node] -> gr a b -> gr a b
    delNodes vs g = foldl' (snd .: flip match) g vs

    -- | Remove multiple 'Edge's from the 'Graph'.
    delEdges :: (DynGraph gr) => [Edge] -> gr a b -> gr a b
    delEdges es g = foldl' (flip delEdge) g es

    -- | Build a 'Graph' from a list of 'Context's.
    --
    --   The list should be in the order such that earlier 'Context's
    --   depend upon later ones (i.e. as produced by @'ufold' (:) []@).
    buildGr :: (DynGraph gr) => [Context a b] -> gr a b
    buildGr = foldr (&) empty

    -- | Build a quasi-unlabeled 'Graph'.
    mkUGraph :: (Graph gr) => [Node] -> [Edge] -> gr () ()
    mkUGraph vs es = mkGraph (labUNodes vs) (labUEdges es)
       where
         labUEdges = map (`toLEdge` ())
         labUNodes = map (flip (,) ())

    -- | Build a graph out of the contexts for which the predicate is
    -- satisfied by recursively calling 'match'.
    gfiltermap :: DynGraph gr => (Context a b -> MContext c d) -> gr a b -> gr c d
    gfiltermap f = ufold (maybe id (&) . f) empty

    -- | Returns the subgraph only containing the labelled nodes which
    -- satisfy the given predicate.
    labnfilter :: Graph gr => (LNode a -> Bool) -> gr a b -> gr a b
    labnfilter p gr = delNodes (map fst . filter (not . p) $ labNodes gr) gr

    -- | Returns the subgraph only containing the nodes which satisfy the
    -- given predicate.
    nfilter :: DynGraph gr => (Node -> Bool) -> gr a b -> gr a b
    nfilter f = labnfilter (f . fst)

    -- | Returns the subgraph only containing the nodes whose labels
    -- satisfy the given predicate.
    labfilter :: DynGraph gr => (a -> Bool) -> gr a b -> gr a b
    labfilter f = labnfilter (f . snd)

    -- | Returns the subgraph induced by the supplied nodes.
    subgraph :: DynGraph gr => [Node] -> gr a b -> gr a b
    subgraph vs = let vs' = IntSet.fromList vs
                  in nfilter (`IntSet.member` vs')

    -- | Find the context for the given 'Node'.  Causes an error if the 'Node' is
    -- not present in the 'Graph'.
    context :: (Graph gr) => gr a b -> Node -> Context a b
    context g v = fromMaybe (error ("Match Exception, Node: "++show v))
                            (fst (match v g))

    -- | Find the label for a 'Node'.
    lab :: (Graph gr) => gr a b -> Node -> Maybe a
    lab g v = fmap lab' . fst $ match v g

    -- | Find the neighbors for a 'Node'.
    neighbors :: (Graph gr) => gr a b -> Node -> [Node]
    neighbors = map snd .: lneighbors

    -- | Find the labelled links coming into or going from a 'Context'.
    lneighbors :: (Graph gr) => gr a b -> Node -> Adj b
    lneighbors = maybe [] lneighbors' .: mcontext

    -- | Find all 'Node's that have a link from the given 'Node'.
    suc :: (Graph gr) => gr a b -> Node -> [Node]
    suc = map snd .: context4l

    -- | Find all 'Node's that link to to the given 'Node'.
    pre :: (Graph gr) => gr a b -> Node -> [Node]
    pre = map snd .: context1l

    -- | Find all 'Node's that are linked from the given 'Node' and the label of
    -- each link.
    lsuc :: (Graph gr) => gr a b -> Node -> [(Node,b)]
    lsuc = map flip2 .: context4l

    -- | Find all 'Node's that link to the given 'Node' and the label of each link.
    lpre :: (Graph gr) => gr a b -> Node -> [(Node,b)]
    lpre = map flip2 .: context1l

    -- | Find all outward-bound 'LEdge's for the given 'Node'.
    out :: (Graph gr) => gr a b -> Node -> [LEdge b]
    out g v = map (\(l,w)->(v,w,l)) (context4l g v)

    -- | Find all inward-bound 'LEdge's for the given 'Node'.
    inn :: (Graph gr) => gr a b -> Node -> [LEdge b]
    inn g v = map (\(l,w)->(w,v,l)) (context1l g v)

    -- | The outward-bound degree of the 'Node'.
    outdeg :: (Graph gr) => gr a b -> Node -> Int
    outdeg = length .: context4l

    -- | The inward-bound degree of the 'Node'.
    indeg :: (Graph gr) => gr a b -> Node -> Int
    indeg  = length .: context1l

    -- | The degree of the 'Node'.
    deg :: (Graph gr) => gr a b -> Node -> Int
    deg = deg' .: context

    -- | The 'Node' in a 'Context'.
    node' :: Context a b -> Node
    node' (_,v,_,_) = v

    -- | The label in a 'Context'.
    lab' :: Context a b -> a
    lab' (_,_,l,_) = l

    -- | The 'LNode' from a 'Context'.
    labNode' :: Context a b -> LNode a
    labNode' (_,v,l,_) = (v,l)

    -- | All 'Node's linked to or from in a 'Context'.
    neighbors' :: Context a b -> [Node]
    neighbors' (p,_,_,s) = map snd p++map snd s

    -- | All labelled links coming into or going from a 'Context'.
    lneighbors' :: Context a b -> Adj b
    lneighbors' (p,_,_,s) = p ++ s

    -- | All 'Node's linked to in a 'Context'.
    suc' :: Context a b -> [Node]
    suc' = map snd . context4l'

    -- | All 'Node's linked from in a 'Context'.
    pre' :: Context a b -> [Node]
    pre' = map snd . context1l'

    -- | All 'Node's linked from in a 'Context', and the label of the links.
    lsuc' :: Context a b -> [(Node,b)]
    lsuc' = map flip2 . context4l'

    -- | All 'Node's linked from in a 'Context', and the label of the links.
    lpre' :: Context a b -> [(Node,b)]
    lpre' = map flip2 . context1l'

    -- | All outward-directed 'LEdge's in a 'Context'.
    out' :: Context a b -> [LEdge b]
    out' c@(_,v,_,_) = map (\(l,w)->(v,w,l)) (context4l' c)

    -- | All inward-directed 'LEdge's in a 'Context'.
    inn' :: Context a b -> [LEdge b]
    inn' c@(_,v,_,_) = map (\(l,w)->(w,v,l)) (context1l' c)

    -- | The outward degree of a 'Context'.
    outdeg' :: Context a b -> Int
    outdeg' = length . context4l'

    -- | The inward degree of a 'Context'.
    indeg' :: Context a b -> Int
    indeg' = length . context1l'

    -- | The degree of a 'Context'.
    deg' :: Context a b -> Int
    deg' (p,_,_,s) = length p+length s

    -- | Checks if there is a directed edge between two nodes.
    hasEdge :: Graph gr => gr a b -> Edge -> Bool
    hasEdge gr (v,w) = w `elem` suc gr v

    -- | Checks if there is an undirected edge between two nodes.
    hasNeighbor :: Graph gr => gr a b -> Node -> Node -> Bool
    hasNeighbor gr v w = w `elem` neighbors gr v

    -- | Checks if there is a labelled edge between two nodes.
    hasLEdge :: (Graph gr, Eq b) => gr a b -> LEdge b -> Bool
    hasLEdge gr (v,w,l) = (w,l) `elem` lsuc gr v

    -- | Checks if there is an undirected labelled edge between two nodes.
    hasNeighborAdj :: (Graph gr, Eq b) => gr a b -> Node -> (b,Node) -> Bool
    hasNeighborAdj gr v a = a `elem` lneighbors gr v

    ----------------------------------------------------------------------
    -- GRAPH EQUALITY
    ----------------------------------------------------------------------

    slabNodes :: (Graph gr) => gr a b -> [LNode a]
    slabNodes = sortBy (compare `on` fst) . labNodes

    glabEdges :: (Graph gr) => gr a b -> [GroupEdges b]
    glabEdges = map (GEs . groupLabels)
                . groupBy ((==) `on` toEdge)
                . sortBy (compare `on` toEdge)
                . labEdges
      where
        groupLabels les = toLEdge (toEdge (head les)) (map edgeLabel les)

    equal :: (Eq a,Eq b,Graph gr) => gr a b -> gr a b -> Bool
    equal g g' = slabNodes g == slabNodes g' && glabEdges g == glabEdges g'
    -- This assumes that nodes aren't repeated (which shouldn't happen for
    -- sane graph instances).  If node IDs are repeated, then the usage of
    -- slabNodes cannot guarantee stable ordering.

    -- Newtype wrapper just to test for equality of multiple edges.  This
    -- is needed because without an Ord constraint on `b' it is not
    -- possible to guarantee a stable ordering on edge labels.
    newtype GroupEdges b = GEs (LEdge [b])
      deriving (Show, Read)

    instance (Eq b) => Eq (GroupEdges b) where
      (GEs (v1,w1,bs1)) == (GEs (v2,w2,bs2)) = v1 == v2
                                               && w1 == w2
                                               && eqLists bs1 bs2

    eqLists :: (Eq a) => [a] -> [a] -> Bool
    eqLists xs ys = null (xs \\ ys) && null (ys \\ xs)
    -- OK to use \\ here as we want each value in xs to cancel a *single*
    -- value in ys.

    ----------------------------------------------------------------------
    -- UTILITIES
    ----------------------------------------------------------------------

    -- auxiliary functions used in the implementation of the
    -- derived class members
    --
    (.:) :: (c -> d) -> (a -> b -> c) -> a -> b -> d
    -- f .: g = \x y->f (g x y)
    -- f .: g = (f .) . g
    -- (.:) f = ((f .) .)
    -- (.:) = (.) (.) (.)
    (.:) = (.) . (.)

    flip2 :: (a,b) -> (b,a)
    flip2 (x,y) = (y,x)

    -- projecting on context elements
    --
    context1l :: (Graph gr) => gr a b -> Node -> Adj b
    context1l = maybe [] context1l' .: mcontext

    context4l :: (Graph gr) => gr a b -> Node -> Adj b
    context4l = maybe [] context4l' .: mcontext

    mcontext :: (Graph gr) => gr a b -> Node -> MContext a b
    mcontext = fst .: flip match

    context1l' :: Context a b -> Adj b
    context1l' (p,v,_,s) = p++filter ((==v).snd) s

    context4l' :: Context a b -> Adj b
    context4l' (p,v,_,s) = s++filter ((==v).snd) p

    ----------------------------------------------------------------------
    -- PRETTY PRINTING
    ----------------------------------------------------------------------

    -- | Pretty-print the graph.  Note that this loses a lot of
    --   information, such as edge inverses, etc.
    prettify :: (DynGraph gr, Show a, Show b) => gr a b -> String
    prettify g = foldr (showsContext . context g) id (nodes g) ""
      where
        showsContext (_,n,l,s) sg = shows n . (':':) . shows l
                                    . showString "->" . shows s
                                    . ('\n':) . sg

    -- | Pretty-print the graph to stdout.
    prettyPrint :: (DynGraph gr, Show a, Show b) => gr a b -> IO ()
    prettyPrint = putStr . prettify

    ----------------------------------------------------------------------
    -- Ordered Graph
    ----------------------------------------------------------------------

    -- | OrdGr comes equipped with an Ord instance, so that graphs can be
    --   used as e.g. Map keys.
    newtype OrdGr gr a b = OrdGr { unOrdGr :: gr a b }
      deriving (Read,Show)

    instance (Graph gr, Ord a, Ord b) => Eq (OrdGr gr a b) where
      g1 == g2 = compare g1 g2 == EQ

    instance (Graph gr, Ord a, Ord b) => Ord (OrdGr gr a b) where
      compare (OrdGr g1) (OrdGr g2) =
        (compare `on` sort . labNodes) g1 g2
        `mappend` (compare `on` sort . labEdges) g1 g2