diff --git a/library/dgraphs.yap b/library/dgraphs.yap
index ed9687de4..d66ead6aa 100644
--- a/library/dgraphs.yap
+++ b/library/dgraphs.yap
@@ -14,10 +14,13 @@
 	    dgraph_del_edges/3,
 	    dgraph_del_vertex/3,
 	    dgraph_del_vertices/3,
+	    dgraph_edge/3,
 	    dgraph_edges/2,
 	    dgraph_vertices/2,
-	    dgraph_neighbors/2,
-	    dgraph_neighbours/2,
+	    dgraph_to_ugraph/2,
+	    ugraph_to_dgraph/2,
+	    dgraph_neighbors/3,
+	    dgraph_neighbours/3,
 	    dgraph_complement/2,
 	    dgraph_transpose/2,
 	    dgraph_compose/3,
@@ -43,7 +46,7 @@
 	 ord_union/3,
 	 ord_subtract/3,
 	 ord_del_element/3,
-	 ord_member/2]).
+	 ord_memberchk/2]).
 
 dgraph_new(Vertices) :-
 	rb_new(Vertices).
@@ -65,7 +68,7 @@ dgraph_add_edges(Edges) -->
 	 all_vertices_in_edges(SortedEdges,Vertices),
 	 sort(Vertices,SortedVertices)
 	},
-	dgraph_add_egdes(SortedVertices,SortedEdges).
+	dgraph_add_edges(SortedVertices,SortedEdges).
 
 all_vertices_in_edges([],[]).
 all_vertices_in_edges([V1-V2|Edges],[V1,V2|Vertices]) :-
@@ -79,14 +82,14 @@ edges2graphl([V|Vertices], SortedEdges, [V-[]|GraphL]) :-
 	edges2graphl(Vertices, SortedEdges, GraphL).
 
 
-dgraph_add_egdes([],[]) --> [].
-dgraph_add_egdes([V|Vs],[V-V1|Es]) --> !,
+dgraph_add_edges([],[]) --> [].
+dgraph_add_edges([V|Vs],[V-V1|Es]) --> !,
 	{ get_extra_children(Es,V,Children,REs) },
 	dgraph_update_vertex(V,[V1|Children]),
-	dgraph_add_egdes(Vs,REs).
-dgraph_add_egdes([V|Vs],Es) --> !,
+	dgraph_add_edges(Vs,REs).
+dgraph_add_edges([V|Vs],Es) --> !,
 	dgraph_update_vertex(V,[]),
-	dgraph_add_egdes(Vs,Es).
+	dgraph_add_edges(Vs,Es).
 
 get_extra_children([V-C|Es],V,[C|Children],REs) :- !,
 	get_extra_children(Es,V,Children,REs).
@@ -266,7 +269,7 @@ transit_graph2([GC|GrandChildren], V, G, [V-GC|NewEdges], MoreEdges) :-
 
 is_edge(V1,V2,G) :-
 	rb_lookup(V1,Children,G),
-	ord_member(Children, V2).
+	ord_memberchk(V2, Children).
 
 dgraph_symmetric_closure(G,S) :-
 	dgraph_edges(G, Edges),
@@ -328,3 +331,15 @@ close_links([l(V,A,A,S,E)|Links], RQ, RQ0) :-
 	close_links(Links, RQ1, RQ0).
 
 
+ugraph_to_dgraph(UG, DG) :-
+	ord_list_to_rbtree(UG, DG).
+
+dgraph_to_ugraph(DG, UG) :-
+	rb_visit(DG, UG).
+
+
+dgraph_edge(N1, N2, G) :-
+	rb_lookup(N1, Ns, G),
+	ord_memberchk(N2, Ns).
+
+
diff --git a/library/rbtrees.yap b/library/rbtrees.yap
index e87659dd9..765aac38c 100644
--- a/library/rbtrees.yap
+++ b/library/rbtrees.yap
@@ -43,7 +43,7 @@
 	   rb_in/3
        ]).
 
-:- meta_predicate rb_map(+,:,-), rb_apply(+,+,:,-).
+:- meta_predicate rb_map(+,:,-), rb_partial_map(+,+,:,-), rb_apply(+,+,:,-).
 
 % create an empty tree.
 rb_new(t(Nil,Nil)) :- Nil = black([],[],[],[]).
@@ -188,9 +188,11 @@ apply(black(Left,Key0,Val0,Right), Key, Goal, black(NewLeft,Key0,Val,NewRight))
 	;
 	Cmp == (>) ->
 	    NewRight = Right,
+	    Val = Val0,
 	    apply(Left, Key, Goal, NewLeft)
 	;
 	    NewLeft = Left,
+	    Val = Val0,
 	    apply(Right, Key, Goal, NewRight)
 	).
 apply(red(Left,Key0,Val0,Right), Key, Goal, red(NewLeft,Key0,Val,NewRight)) :-
@@ -202,9 +204,11 @@ apply(red(Left,Key0,Val0,Right), Key, Goal, red(NewLeft,Key0,Val,NewRight)) :-
 	;
 	Cmp == (>) ->
 	    NewRight = Right,
+	    Val = Val0,
 	    apply(Left, Key, Goal, NewLeft)
 	;
 	    NewLeft = Left,
+	    Val = Val0,
 	    apply(Right, Key, Goal, NewRight)
 	).
 
@@ -635,15 +639,31 @@ clone(black(L,K,_,R),black(NL,K,NV,NR),NsF,Ns0) :-
 	clone(R,NR,Ns1,Ns0).
 
 rb_partial_map(t(Nil,T0), Map, Goal, t(Nil,TF)) :-
-	partial_map(T0, Map, [], Goal, TF).
+	partial_map(T0, Map, [], Nil, Goal, TF).
 
 rb_partial_map(t(Nil,T0), Map, Map0, Goal, t(Nil,TF)) :-
-	rb_partial_map(T0, Map, Map0, Goal, TF).
+	rb_partial_map(T0, Map, Map0, Nil, Goal, TF).
 
-partial_map(T,[],[],_,T) :- !.
-partial_map(black([],[],[],[]),Map,Map,_,black([],[],[],[])) :- !.
-partial_map(red(L,K,V,R),Map,MapF,Goal,red(NL,K,NV,NR)) :-
-	partial_map(L,Map,MapI,Goal,NL),
+partial_map(T,[],[],_,_,T) :- !.
+partial_map(black([],_,_,_),Map,Map,Nil,_,Nil) :- !.
+partial_map(red(L,K,V,R),Map,MapF,Nil,Goal,red(NL,K,NV,NR)) :-
+	partial_map(L,Map,MapI,Nil,Goal,NL),
+	( 
+	    Map == [] -> 
+	    NR = R, NV = V
+	;
+	   MapI = [K1|MapR],
+	   (
+	     K == K1 ->
+	        once(call(Goal,V,NV)),
+	        Map2 = MapR
+	    ;
+	        Map2 = [K1|MapR], NV = V
+	    ),
+	    partial_map(R,Map2,MapF,Nil,Goal,NR)
+	).
+partial_map(black(L,K,V,R),Map,MapF,Nil,Goal,black(NL,K,NV,NR)) :-
+	partial_map(L,Map,MapI,Nil,Goal,NL),
 	( 
 	    MapI == [] -> 
 	    NR = R, NV = V
@@ -655,25 +675,9 @@ partial_map(red(L,K,V,R),Map,MapF,Goal,red(NL,K,NV,NR)) :-
 	        Map2 = MapR
 	    ;
 	        Map2 = [K1|MapR], NV = V
-	    )
-	),
-	partial_map(R,Map2,MapF,Goal,NR).
-partial_map(black(L,K,V,R),Map,MapF,Goal,black(NL,K,NV,NR)) :-
-	partial_map(L,Map,MapI,Goal,NL),
-	( 
-	    MapI == [] -> 
-	    NR = R, NV = V
-	;
-	   MapI = [K1|MapR],
-	   (
-	     K == K1 ->
-	        once(call(Goal,V,NV)),
-	        Map2 = MapR
-	    ;
-	        Map2 = [K1|MapR], NV = V
-	    )
-	),
-	partial_map(R,Goal,Map2,MapF,NR).
+	    ),
+	    partial_map(R,Map2,MapF,Nil,Goal,NR)
+	).
 
 
 %
diff --git a/library/undgraphs.yap b/library/undgraphs.yap
index a248b876f..1f211ea41 100644
--- a/library/undgraphs.yap
+++ b/library/undgraphs.yap
@@ -14,11 +14,13 @@
 	    undgraph_del_edges/3,
 	    undgraph_del_vertex/3,
 	    undgraph_del_vertices/3,
+	    undgraph_edge/3,
 	    undgraph_edges/2,
 	    undgraph_vertices/2,
-	    undgraph_neighbors/2,
-	    undgraph_neighbours/2,
-	    undgraph_complement/2]).
+	    undgraph_neighbors/3,
+	    undgraph_neighbours/3,
+	    undgraph_complement/2,
+	    dgraph_to_undgraph/2]).
 
 :- use_module( library(dgraphs),
 	   [
@@ -31,11 +33,13 @@
 	    dgraph_del_edges/3,
 	    dgraph_del_vertex/3,
 	    dgraph_del_vertices/3,
+	    dgraph_edge/3,
 	    dgraph_edges/2,
 	    dgraph_vertices/2,
-	    dgraph_neighbors/2,
-	    dgraph_neighbours/2,
-	    dgraph_complement/2]).
+	    dgraph_neighbors/3,
+	    dgraph_neighbours/3,
+	    dgraph_complement/2,
+	    dgraph_symmetric_closure/2]).
 
 :- use_module(library(ordsets),
 	[ ord_del_element/3,
@@ -43,7 +47,9 @@
 	  ord_subtract/3]).
 
 :- use_module(library(rbtrees),
-	[ rb_delete/4]).
+	[  rb_delete/4,
+	   rb_partial_map/4
+	]).
 
 undgraph_new(Vertices) :-
 	dgraph_new(Vertices).
@@ -54,7 +60,7 @@ undgraph_add_edge(V1,V2,Vs0,Vs2) :-
 	
 undgraph_add_edges(Edges) -->
 	{ dup_edges(Edges, DupEdges) },
-	dgraph_add_edges(Edges).
+	dgraph_add_edges(DupEdges).
 
 dup_edges([],[]).
 dup_edges([E1-E2|Edges], [E1-E2,E2-E1|DupEdges]) :-
@@ -84,10 +90,22 @@ undgraph_vertices(Vs,Vertices) :-
 
 undgraph_neighbours(V,Vertices,Children) :-
 	dgraph_neighbours(V,Vertices,Children0),
-	ord_del_element(V,Children0,Children).
+	(
+	    ord_del_element(Children0,V,Children)
+	->
+	    true
+	;
+	    Children = Children0
+	).
 undgraph_neighbors(V,Vertices,Children) :-
 	dgraph_neighbors(V,Vertices,Children0),
-	ord_del_element(V,Children0,Children).
+	(
+	    ord_del_element(Children0,V,Children)
+	->
+	    true
+	;
+	    Children = Children0
+	).
 
 undgraph_complement(Vs0,VsF) :-
 	dgraph_complement(Vs0,VsF).
@@ -104,7 +122,13 @@ undgraph_del_edges(Edges) -->
 
 undgraph_del_vertex(V, Vs0, Vsf) :-
 	rb_delete(Vs0, V, BackEdges, Vsi),
-	ord_del_element(BackEdges,V,RealBackEdges),
+	(
+	    ord_del_element(BackEdges,V,RealBackEdges)
+	->
+	    true
+	;
+	    BackEdges = RealBackEdges
+	),
 	rb_partial_map(Vsi, RealBackEdges, del_edge(V), Vsf).
 
 undgraph_del_vertices(Vs) -->
@@ -127,7 +151,13 @@ delete_remaining_edges(SortedVs, TrueBackEdges, Vs0,Vsf) :-
 del_edges(ToRemove,E0,E) :-
 	ord_subtract(E0,ToRemove,E).
 
-del_edges(ToRemove,E0,E) :-
+del_edge(ToRemove,E0,E) :-
 	ord_del_element(E0,ToRemove,E).
 
+dgraph_to_undgraph(G, U) :-
+	dgraph_symmetric_closure(G, U).
+
+undgraph_edge(N1, N2, G) :-
+	dgraph_edge(N1, N2, G).
+