diff --git a/doc/attr.xml b/doc/attr.xml
index 3a6769da8..42649c41b 100644
--- a/doc/attr.xml
+++ b/doc/attr.xml
@@ -138,6 +138,28 @@ gap> DigraphNrEdges(D);
 </ManSection>
 <#/GAPDoc>
 
+<#GAPDoc Label="DigraphNrAdjacencies">
+<ManSection>
+  <Attr Name="DigraphNrAdjacencies" Arg="digraph" />
+  <Returns>An integer.</Returns>
+  <Description> Returns the number of pairs of adjacent vertices of the digraph <A>digraph</A>. This
+    function is agnostic to the direction of an edge, so if <A>digraph</A> constains both the edges <M>(a,
+    b)</M> and <M>(b, a)</M>, this only counts as one adjacency. The following equality holds for
+    any digraph <C>D</C> with no multiple edges: <C>DigraphNrAdjacencies(D) * 2 - DigraphNrLoops(D)
+    = DigraphNrEdges(DigraphSymmetricClosure(D))</C>
+    <Example><![CDATA[
+gap> gr := Digraph([
+> [1, 3, 4, 5], [1, 2, 3, 5], [2, 4, 5], [2, 4, 5], [1]]);;
+gap> DigraphNrAdjacencies(gr);
+13
+gap> DigraphNrAdjacencies(gr) * 2 - DigraphNrLoops(gr) =
+> DigraphNrEdges(DigraphSymmetricClosure(gr));
+true
+]]></Example>
+  </Description>
+</ManSection>
+<#/GAPDoc>
+
 <#GAPDoc Label="DigraphNrLoops">
 <ManSection>
   <Attr Name="DigraphNrLoops" Arg="digraph"/>
diff --git a/doc/z-chap4.xml b/doc/z-chap4.xml
index 0f2ebe1ee..79113ce92 100644
--- a/doc/z-chap4.xml
+++ b/doc/z-chap4.xml
@@ -4,6 +4,7 @@
     <#Include Label="DigraphNrVertices">
     <#Include Label="DigraphEdges">
     <#Include Label="DigraphNrEdges">
+    <#Include Label="DigraphNrAdjacencies">
     <#Include Label="DigraphNrLoops">
     <#Include Label="DigraphSinks">
     <#Include Label="DigraphSources">
diff --git a/gap/attr.gi b/gap/attr.gi
index 68fdd903c..3078cdd72 100644
--- a/gap/attr.gi
+++ b/gap/attr.gi
@@ -701,8 +701,8 @@ function(D)
   return m;
 end);
 
-InstallMethod(DigraphNrAdjacencies, "for a digraph", [IsDigraphByOutNeighboursRep],
-DIGRAPH_NRADJACENCIES);
+InstallMethod(DigraphNrAdjacencies, "for a digraph",
+[IsDigraphByOutNeighboursRep], DIGRAPH_NRADJACENCIES);
 
 InstallMethod(DigraphNrLoops,
 "for a digraph by out-neighbours",
diff --git a/gap/planar.gi b/gap/planar.gi
index 386e5c180..0d7f85cd0 100644
--- a/gap/planar.gi
+++ b/gap/planar.gi
@@ -30,95 +30,50 @@
 # 1. Attributes
 ########################################################################
 
-InstallMethod(PlanarEmbedding, "for a digraph", [IsDigraph],
+HasTrivialRotaionSystem :=
 function(D)
-  local C;
+  if IsMultiDigraph(D) then
+    ErrorNoReturn("expected a digraph with no multiple edges");
+  fi;
   if HasIsPlanarDigraph(D) and not IsPlanarDigraph(D) then
-    return fail;
+    return false;
   fi;
-  C := DigraphMutableCopy(D);
-  DigraphRemoveAllMultipleEdges(C);
-  DigraphRemoveLoops(C);
-  if IsEmptyDigraph(C) or DigraphNrVertices(C) < 3 then
-    return OutNeighbors(C);
+  if DigraphNrVertices(D) < 3 then
+    return true;
   fi;
-  return PLANAR_EMBEDDING(C);
-end);
+  return DigraphNrAdjacencies(D) = DigraphNrLoops(D);
+end;
 
-InstallMethod(OuterPlanarEmbedding, "for a digraph", [IsDigraph],
+InstallMethod(PlanarEmbedding, "for a digraph", [IsDigraph],
 function(D)
-  local C;
-  if HasIsPlanarDigraph(D) and not IsPlanarDigraph(D) then
-    return fail;
-  fi;
-  C := DigraphMutableCopy(D);
-  DigraphRemoveAllMultipleEdges(C);
-  DigraphRemoveLoops(C);
-  if IsEmptyDigraph(C) or DigraphNrVertices(C) < 3 then
-    return OutNeighbors(C);
+  if HasTrivialRotaionSystem(D) then;
+    return OutNeighbors(D);
   fi;
-  return OUTER_PLANAR_EMBEDDING(C);
+  return PLANAR_EMBEDDING(D);
 end);
 
-InstallMethod(KuratowskiPlanarSubdigraph, "for a digraph", [IsDigraph],
+InstallMethod(OuterPlanarEmbedding, "for a digraph", [IsDigraph],
 function(D)
-  local C;
-  C := DigraphMutableCopy(D);
-  DigraphRemoveAllMultipleEdges(C);
-  DigraphRemoveLoops(C);
-  if IsPlanarDigraph(C) then
-    return fail;
+  if HasTrivialRotaionSystem(D) then;
+    return OutNeighbors(D);
   fi;
-  return KURATOWSKI_PLANAR_SUBGRAPH(C);
+  return OUTER_PLANAR_EMBEDDING(D);
 end);
 
+InstallMethod(KuratowskiPlanarSubdigraph, "for a digraph", [IsDigraph],
+KURATOWSKI_PLANAR_SUBGRAPH);
+
 InstallMethod(KuratowskiOuterPlanarSubdigraph, "for a digraph", [IsDigraph],
-function(D)
-  local C;
-  C := DigraphMutableCopy(D);
-  DigraphRemoveAllMultipleEdges(C);
-  DigraphRemoveLoops(C);
-  if IsOuterPlanarDigraph(C) then
-    return fail;
-  fi;
-  return KURATOWSKI_OUTER_PLANAR_SUBGRAPH(C);
-end);
+KURATOWSKI_OUTER_PLANAR_SUBGRAPH);
 
 InstallMethod(SubdigraphHomeomorphicToK23, "for a digraph", [IsDigraph],
-function(D)
-  local C;
-  C := DigraphMutableCopy(D);
-  DigraphRemoveAllMultipleEdges(C);
-  DigraphRemoveLoops(C);
-  if IsOuterPlanarDigraph(C) then
-    return fail;
-  fi;
-  return SUBGRAPH_HOMEOMORPHIC_TO_K23(C);
-end);
+SUBGRAPH_HOMEOMORPHIC_TO_K23);
 
 InstallMethod(SubdigraphHomeomorphicToK4, "for a digraph", [IsDigraph],
-function(D)
-  local C;
-  C := DigraphMutableCopy(D);
-  DigraphRemoveAllMultipleEdges(C);
-  DigraphRemoveLoops(C);
-  if IsOuterPlanarDigraph(C) then
-    return fail;
-  fi;
-  return SUBGRAPH_HOMEOMORPHIC_TO_K4(D);
-end);
+SUBGRAPH_HOMEOMORPHIC_TO_K4);
 
 InstallMethod(SubdigraphHomeomorphicToK33, "for a digraph", [IsDigraph],
-function(D)
-  local C;
-  C := DigraphMutableCopy(D);
-  DigraphRemoveAllMultipleEdges(C);
-  DigraphRemoveLoops(C);
-  if IsPlanarDigraph(C) then
-    return fail;
-  fi;
-  return SUBGRAPH_HOMEOMORPHIC_TO_K33(C);
-end);
+SUBGRAPH_HOMEOMORPHIC_TO_K33);
 
 ########################################################################
 # 2. Properties
@@ -126,33 +81,32 @@ end);
 
 InstallMethod(IsPlanarDigraph, "for a digraph", [IsDigraph],
 function(D)
-  local C, v, e;
-  C := MaximalAntiSymmetricSubdigraph(DigraphMutableCopyIfMutable(D));
+  local v, n_antisymmetric_edges;
   v := DigraphNrVertices(D);
-  e := DigraphNrEdges(C);
-  if v < 5 or e < 9 then
+  n_antisymmetric_edges := DigraphNrAdjacencies(D) - DigraphNrLoops(D);
+  if v < 5 or n_antisymmetric_edges < 9 then
     return true;
-  elif (IsConnectedDigraph(D) and e > 3 * v - 6)
+  elif (IsConnectedDigraph(D) and n_antisymmetric_edges > 3 * v - 6)
       or (HasChromaticNumber(D) and ChromaticNumber(D) > 4) then
     return false;
   fi;
-  return IS_PLANAR(C);
+  return IS_PLANAR(D);
 end);
 
 InstallMethod(IsOuterPlanarDigraph, "for a digraph", [IsDigraph],
 function(D)
-  local C, v, e;
+  local v, n_antisymmetric_edges;
   if HasIsPlanarDigraph(D) and not IsPlanarDigraph(D) then
     return false;
   fi;
   v := DigraphNrVertices(D);
-  e := DigraphNrEdges(D);
-  if v < 4 or e < 6 then
+  n_antisymmetric_edges := DigraphNrAdjacencies(D) - DigraphNrLoops(D);
+
+  if v < 4 or n_antisymmetric_edges < 6 then
     return true;
   elif HasChromaticNumber(D) and ChromaticNumber(D) > 3 then
     # Outer planar graphs are 3-colourable
     return false;
   fi;
-  C := DigraphMutableCopyIfMutable(D);
-  return IS_OUTER_PLANAR(MaximalAntiSymmetricSubdigraph(C));
+  return IS_OUTER_PLANAR(D);
 end);
diff --git a/src/digraphs.c b/src/digraphs.c
index 2a397b7d5..90183ccef 100644
--- a/src/digraphs.c
+++ b/src/digraphs.c
@@ -148,7 +148,7 @@ Int DigraphNrAdjacencies(Obj D) {
       Obj const out_v = ELM_LIST(out, v);
       for (Int w = 1; w <= LEN_LIST(out_v); ++w) {
         Int u = INT_INTOBJ(ELM_LIST(out_v, w));
-        if (v < u
+        if (v <= u
             || CALL_3ARGS(IsDigraphEdge, D, INTOBJ_INT(u), INTOBJ_INT(v))
                    == False) {
           ++nr;
diff --git a/src/planar.c b/src/planar.c
index c36071a79..57bc95cd0 100644
--- a/src/planar.c
+++ b/src/planar.c
@@ -147,16 +147,10 @@ Obj boyers_planarity_check(Obj digraph, int flags, bool krtwsk) {
 
   if (gp_InitGraph(theGraph, V) != OK) {
     gp_Free(&theGraph);
-    ErrorQuit("Digraphs: boyers_planarity_check (C): invalid number of nodes!",
-              0L,
-              0L);
-    return 0L;
+    return Fail;
   } else if (gp_EnsureArcCapacity(theGraph, 2 * E) != OK) {
     gp_Free(&theGraph);
-    ErrorQuit("Digraphs: boyers_planarity_check (C): invalid number of edges!",
-              0L,
-              0L);
-    return 0L;
+    return Fail;
   }
 
   switch (flags) {
diff --git a/tst/standard/attr.tst b/tst/standard/attr.tst
index 167efe8be..a51a6bed2 100644
--- a/tst/standard/attr.tst
+++ b/tst/standard/attr.tst
@@ -192,6 +192,12 @@ gap> AdjacencyMatrix(Digraph(rec(DigraphNrVertices := 0,
 >                                DigraphRange      := [])));
 [  ]
 
+#  DigraphNrAdjacencies
+gap> G := RandomDigraph(50);;
+gap> DigraphNrAdjacencies(G) * 2 - DigraphNrLoops(G) = 
+> DigraphNrEdges(DigraphSymmetricClosure(G));
+true
+
 #  DigraphTopologicalSort
 gap> r := rec(DigraphNrVertices := 20000,
 >             DigraphSource     := [],
diff --git a/tst/standard/examples.tst b/tst/standard/examples.tst
index e3307afbd..938397521 100644
--- a/tst/standard/examples.tst
+++ b/tst/standard/examples.tst
@@ -249,6 +249,8 @@ gap> DigraphNrVertices(D);
 8
 gap> DigraphNrEdges(D);
 26
+gap> DigraphNrAdjacencies(D);
+13
 gap> DigraphUndirectedGirth(D);
 3
 gap> LollipopGraph(IsMutableDigraph, 5, 3);
diff --git a/tst/standard/planar.tst b/tst/standard/planar.tst
index 80bf205fa..c8f4c8ecf 100644
--- a/tst/standard/planar.tst
+++ b/tst/standard/planar.tst
@@ -235,9 +235,9 @@ gap> IS_PLANAR(2);
 Error, Digraphs: boyers_planarity_check (C): the 1st argument must be a digrap\
 h, not integer
 gap> IS_PLANAR(NullDigraph(0));
-Error, Digraphs: boyers_planarity_check (C): invalid number of nodes!
+fail
 gap> IS_PLANAR(NullDigraph(70000));
-Error, Digraphs: boyers_planarity_check (C): invalid number of edges!
+fail
 gap> IsPlanarDigraph(NullDigraph(70000));
 true
 gap> IS_PLANAR(CompleteDigraph(2));
diff --git a/tst/testinstall.tst b/tst/testinstall.tst
index e165c78c2..0012bcd8e 100644
--- a/tst/testinstall.tst
+++ b/tst/testinstall.tst
@@ -246,9 +246,13 @@ gap> gr := DigraphRemoveEdge(gr, [1, 2]);;
 gap> gr := DigraphRemoveEdges(gr, [[1, 2], [2, 1]]);;
 gap> DigraphNrEdges(gr);
 40
+gap> DigraphNrAdjacencies(gr);
+20
 gap> gr2 := DigraphClosure(gr, 7);;
 gap> DigraphNrEdges(gr2);
 42
+gap> DigraphNrAdjacencies(gr2);
+21
 
 #  Fix seg fault cause by wrong handling of no edges in
 # FuncDIGRAPH_SOURCE_RANGE