diff --git a/gap/attr.gi b/gap/attr.gi
index 67bb792ac..de37f4618 100644
--- a/gap/attr.gi
+++ b/gap/attr.gi
@@ -1630,11 +1630,13 @@ function(D)
         return [C, blocked];
     end;
 
-    digraph := DigraphSymmetricClosure(DigraphRemoveLoops(
-        DigraphRemoveAllMultipleEdges(DigraphMutableCopyIfMutable(D))));
-
+    digraph := DigraphMutableCopy(D);
+    DigraphSymmetricClosure(DigraphRemoveLoops(
+                 DigraphRemoveAllMultipleEdges(digraph)));
+    MakeImmutable(digraph);
     SetDigraphVertexLabels(digraph,
                  Reversed(DigraphDegeneracyOrdering(digraph)));
+
     temp := Triplets(digraph);
     T := temp[1];
     C := temp[2];
diff --git a/tst/standard/attr.tst b/tst/standard/attr.tst
index 3d79a8c5f..468abcd59 100644
--- a/tst/standard/attr.tst
+++ b/tst/standard/attr.tst
@@ -1036,6 +1036,41 @@ gap> DigraphAllChordlessCycles(D);
   [ 1, 4, 8, 7, 6, 2 ], [ 1, 4, 3, 2 ], [ 1, 4, 3, 7, 6, 5 ], [ 3, 2, 6, 7 ], 
   [ 2, 1, 5, 6 ], [ 2, 1, 5, 8, 7, 3 ] ]
 
+# check that DigraphAllChordlessCycles do not change the input graph
+gap> g := Digraph([[2, 3, 7], [1, 4, 8], [1, 4, 9], [2, 3, 10], [6, 7, 9], [5, 8, 10],
+>                  [8, 5, 1], [7, 6, 2], [5, 10, 3], [6, 9, 4]]);;
+gap> DigraphAllChordlessCycles(g);
+[ [ 7, 8, 6, 5 ], [ 6, 5, 9, 10 ], [ 3, 4, 10, 6, 5, 7, 1 ], 
+  [ 3, 4, 10, 6, 8, 7, 1 ], [ 3, 4, 10, 9 ], [ 2, 4, 10, 6, 5, 7, 1 ], 
+  [ 2, 4, 10, 6, 8 ], [ 2, 4, 10, 9, 5, 7, 8 ], [ 2, 4, 10, 9, 5, 7, 1 ], 
+  [ 3, 4, 2, 1 ], [ 3, 4, 2, 8, 7, 5, 9 ], [ 3, 4, 2, 8, 6, 5, 9 ], 
+  [ 3, 1, 7, 8, 6, 10, 9 ], [ 3, 1, 7, 5, 9 ], [ 2, 1, 7, 8 ], 
+  [ 3, 1, 2, 8, 6, 5, 9 ], [ 3, 1, 2, 8, 6, 10, 9 ] ]
+gap> DigraphAllUndirectedSimpleCircuits(g);
+[ [ 1, 2, 4, 3 ], [ 1, 2, 4, 3, 9, 5, 6, 8, 7 ], [ 1, 2, 4, 3, 9, 5, 7 ], 
+  [ 1, 2, 4, 3, 9, 10, 6, 5, 7 ], [ 1, 2, 4, 3, 9, 10, 6, 8, 7 ], 
+  [ 1, 2, 4, 10, 6, 5, 7 ], [ 1, 2, 4, 10, 6, 5, 9, 3 ], 
+  [ 1, 2, 4, 10, 6, 8, 7 ], [ 1, 2, 4, 10, 6, 8, 7, 5, 9, 3 ], 
+  [ 1, 2, 4, 10, 9, 3 ], [ 1, 2, 4, 10, 9, 5, 6, 8, 7 ], 
+  [ 1, 2, 4, 10, 9, 5, 7 ], [ 1, 2, 8, 6, 5, 7 ], [ 1, 2, 8, 6, 5, 9, 3 ], 
+  [ 1, 2, 8, 6, 5, 9, 10, 4, 3 ], [ 1, 2, 8, 6, 10, 4, 3 ], 
+  [ 1, 2, 8, 6, 10, 4, 3, 9, 5, 7 ], [ 1, 2, 8, 6, 10, 9, 3 ], 
+  [ 1, 2, 8, 6, 10, 9, 5, 7 ], [ 1, 2, 8, 7 ], [ 1, 2, 8, 7, 5, 6, 10, 4, 3 ],
+  [ 1, 2, 8, 7, 5, 6, 10, 9, 3 ], [ 1, 2, 8, 7, 5, 9, 3 ], 
+  [ 1, 2, 8, 7, 5, 9, 10, 4, 3 ], [ 1, 3, 4, 2, 8, 6, 5, 7 ], 
+  [ 1, 3, 4, 2, 8, 6, 10, 9, 5, 7 ], [ 1, 3, 4, 2, 8, 7 ], 
+  [ 1, 3, 4, 10, 6, 5, 7 ], [ 1, 3, 4, 10, 6, 8, 7 ], 
+  [ 1, 3, 4, 10, 9, 5, 6, 8, 7 ], [ 1, 3, 4, 10, 9, 5, 7 ], 
+  [ 1, 3, 9, 5, 6, 8, 7 ], [ 1, 3, 9, 5, 6, 10, 4, 2, 8, 7 ], 
+  [ 1, 3, 9, 5, 7 ], [ 1, 3, 9, 10, 4, 2, 8, 6, 5, 7 ], 
+  [ 1, 3, 9, 10, 4, 2, 8, 7 ], [ 1, 3, 9, 10, 6, 5, 7 ], 
+  [ 1, 3, 9, 10, 6, 8, 7 ], [ 2, 4, 3, 9, 5, 6, 8 ], [ 2, 4, 3, 9, 5, 7, 8 ], 
+  [ 2, 4, 3, 9, 10, 6, 5, 7, 8 ], [ 2, 4, 3, 9, 10, 6, 8 ], 
+  [ 2, 4, 10, 6, 5, 7, 8 ], [ 2, 4, 10, 6, 8 ], [ 2, 4, 10, 9, 5, 6, 8 ], 
+  [ 2, 4, 10, 9, 5, 7, 8 ], [ 4, 3, 9, 5, 6, 10 ], 
+  [ 4, 3, 9, 5, 7, 8, 6, 10 ], [ 4, 3, 9, 10 ], [ 5, 6, 8, 7 ], 
+  [ 9, 5, 6, 10 ], [ 9, 5, 7, 8, 6, 10 ] ]
+
 #  Issue #676
 gap> D := Digraph([[], [3], []]);;
 gap> SetDigraphVertexLabels(D, ["one", "two", "three"]);