Added method AllUndirectedSimpleCircuits

doc/attr.xml

@@ -1374,6 +1374,46 @@ gap> DigraphLongestSimpleCircuit(D);
 </ManSection>
 <#/GAPDoc>
 
+<#GAPDoc Label="DigraphAllUndirectedSimpleCircuits">
+<ManSection>
+  <Attr Name="DigraphAllUndirectedSimpleCircuits" Arg="digraph"/>
+  <Returns>A list of lists of vertices.</Returns>
+  <Description>
+    If <A>digraph</A> is a digraph, then <C>DigraphAllUndirectedSimpleCircuits</C>
+    returns a list of the <E> undirected simple circuits</E> in <A>digraph</A>. <P/>
+
+    See Section <Ref Subsect="Definitions" Style="Number" /> for the definition
+    of a simple circuit, and related notions. Note that a loop is a simple
+    circuit. A simple circuit is undirected if the orientation of the edges
+    in the circuit does not matter.<P/>
+
+    The attribute <C>DigraphAllUndirectedSimpleCircuitss</C> ignores
+    multiple edges, and identifies a undirected simple circuit using only its subsequence
+    of vertices.
+    See Section <Ref Subsect="DigraphAllSimpleCircuits" Style="Number" /> for more details
+    on simple circuits.<P/>
+
+    <Example><![CDATA[
+gap> D := ChainDigraph(10);;
+gap> DigraphAllUndirectedSimpleCircuits(D);
+[  ]
+gap> D := Digraph([[1, 1]]);
+<immutable multidigraph with 1 vertex, 2 edges>
+gap> DigraphAllUndirectedSimpleCircuits(D);
+[ [ 1 ] ]
+gap> D := CycleDigraph(IsMutableDigraph, 3);
+<mutable digraph with 3 vertices, 3 edges>
+gap> DigraphAllUndirectedSimpleCircuits(D);
+[ [ 1, 2, 3 ] ]
+gap> D := DigraphSymmetricClosure(CycleDigraph(IsMutableDigraph, 3));
+<mutable digraph with 3 vertices, 6 edges>
+gap> DigraphAllUndirectedSimpleCircuits(D);
+[ [ 1, 2, 3 ] ]
+]]></Example>
+  </Description>
+</ManSection>
+<#/GAPDoc>
+
 <#GAPDoc Label="DigraphAllChordlessCycles">
 <ManSection>
   <Attr Name="DigraphAllChordlessCycles" Arg="digraph"/>

doc/z-chap4.xml

@@ -76,6 +76,7 @@
     <#Include Label="IteratorOfPaths">
     <#Include Label="DigraphAllSimpleCircuits">
     <#Include Label="DigraphLongestSimpleCircuit">
+    <#Include Label="DigraphAllUndirectedSimpleCircuits">
     <#Include Label="DigraphAllChordlessCycles">
     <#Include Label="DigraphLayers">
     <#Include Label="DigraphDegeneracy">

gap/attr.gd

@@ -58,6 +58,7 @@ DeclareAttribute("DigraphAbsorptionExpectedSteps", IsDigraph);
 
 DeclareAttribute("DigraphAllSimpleCircuits", IsDigraph);
 DeclareAttribute("DigraphLongestSimpleCircuit", IsDigraph);
+DeclareAttribute("DigraphAllUndirectedSimpleCircuits", IsDigraph);
 DeclareAttribute("DigraphAllChordlessCycles", IsDigraph);
 DeclareAttribute("HamiltonianPath", IsDigraph);
 DeclareAttribute("DigraphPeriod", IsDigraph);

gap/attr.gi

@@ -1524,6 +1524,26 @@ function(D)
   return Concatenation(loops, out);
 end);
 
+# Compute all undirected simple circuits by filtering the output
+# of DigraphAllSimpleCircuits
+InstallMethod(DigraphAllUndirectedSimpleCircuits, "for a digraph", [IsDigraph],
+function(D)
+  local digraph, cycles, keep, cycle, cycleRev;
+  digraph := DigraphSymmetricClosure(
+      DigraphRemoveAllMultipleEdges(DigraphMutableCopyIfMutable(D)));
+  cycles := Filtered(DigraphAllSimpleCircuits(digraph),
+    c -> Length(c) > 2 or Length(c) = 1);
+  keep := HashSet();
+  for cycle in cycles do
+    cycleRev := [cycle[1]];
+    Append(cycleRev, Reversed(cycle{[2 .. Length(cycle)]}));
+    if (not cycle in keep and not cycleRev in keep) or Length(cycle) = 1 then
+      AddSet(keep, cycle);
+    fi;
+  od;
+  return Set(keep);
+end);
+
 # Compute all chordless cycles for a given symmetric digraph
 # Algorithm based on https://arxiv.org/pdf/1404.7610
 InstallMethod(DigraphAllChordlessCycles, "for a digraph",

tst/standard/attr.tst

@@ -948,6 +948,37 @@ gap> gr := Digraph([[3, 6, 7], [3, 6, 8], [1, 2, 3, 6, 7, 8],
 gap> Length(DigraphAllSimpleCircuits(gr));
 259
 
+#  DigraphAllUndirectedSimpleCircuits
+gap> gr := Digraph([]);;
+gap> DigraphAllUndirectedSimpleCircuits(gr);
+[  ]
+gap> gr := ChainDigraph(4);;
+gap> DigraphAllUndirectedSimpleCircuits(gr);
+[  ]
+gap> gr := CompleteDigraph(2);;
+gap> DigraphAllUndirectedSimpleCircuits(gr);
+[  ]
+gap> gr := CompleteDigraph(3);;
+gap> DigraphAllUndirectedSimpleCircuits(gr);
+[ [ 1, 2, 3 ] ]
+gap> gr := Digraph([[], [3], [2, 4], [5, 4], [4]]);
+<immutable digraph with 5 vertices, 6 edges>
+gap> DigraphAllUndirectedSimpleCircuits(gr);
+[ [ 4 ] ]
+gap> gr := Digraph([[1, 2], [2, 1]]);
+<immutable digraph with 2 vertices, 4 edges>
+gap> DigraphAllUndirectedSimpleCircuits(gr);
+[ [ 1 ], [ 2 ] ]
+gap> gr := Digraph([[4], [1, 3], [1, 2], [2, 3]]);;
+gap> DigraphAllUndirectedSimpleCircuits(gr);
+[ [ 1, 2, 3 ], [ 1, 2, 3, 4 ], [ 1, 2, 4 ], [ 1, 2, 4, 3 ], [ 1, 3, 2, 4 ], 
+  [ 1, 3, 4 ], [ 2, 3, 4 ] ]
+gap> gr := Digraph([[3, 6, 7], [3, 6, 8], [1, 2, 3, 6, 7, 8],
+> [2, 3, 4, 8], [2, 3, 4, 5, 6, 7], [1, 3, 4, 5, 7], [2, 3, 6, 8],
+> [1, 2, 3, 8]]);;
+gap> Length(DigraphAllUndirectedSimpleCircuits(gr));
+1330
+
 # DigraphAllChordlessCycles
 gap> gr := Digraph([]);;
 gap> DigraphAllChordlessCycles(gr);