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Graphs: fix isCyclic Digraph #3628

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Graphs: fix isCyclic Digraph #3628

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49 changes: 30 additions & 19 deletions M2/Macaulay2/packages/Graphs.m2
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Original file line number Diff line number Diff line change
Expand Up @@ -1154,16 +1154,7 @@ spectrum Graph := List => G -> sort toList eigenvalues (adjacencyMatrix G, Hermi



topologicalSort = method(TypicalValue =>List)
topologicalSort Digraph := List => D -> topologicalSort(D, "")
topologicalSort (Digraph, String) := List => (D,s) -> (
if instance(D, Graph) or isCyclic D then error "Topological sorting is only defined for acyclic directed graphs.";
s = toLower s;
processor := if s == "random" then random
else if s == "min" then sort
else if s == "max" then rsort
else if s == "degree" then L -> last \ sort transpose {apply(L, v -> degree(D, v)), L}
else identity;
attemptTopologicalSort = (D,processor) -> (
S := processor sources D;
L := {};
v := null;
Expand All @@ -1172,7 +1163,23 @@ topologicalSort (Digraph, String) := List => (D,s) -> (
L = L|{v};
S = processor join(drop(S, 1), select(toList children (D, v), c -> isSubset(parents(D, c), L)));
);
L
if #L == #(vertexSet D) then L else null
)

topologicalSort = method(TypicalValue =>List)
topologicalSort Digraph := List => D -> topologicalSort(D, "")
topologicalSort (Digraph, String) := List => (D,s) -> (
if instance(D, Digraph) then (
s = toLower s;
processor := if s == "random" then random
else if s == "min" then sort
else if s == "max" then rsort
else if s == "degree" then L -> last \ sort transpose {apply(L, v -> degree(D, v)), L}
else identity;
L := attemptTopologicalSort(D, processor);
if L =!= null then return L;
);
error "Topological sorting is only defined for acyclic directed graphs.";
)


Expand Down Expand Up @@ -1270,14 +1277,7 @@ isConnected Graph := Boolean => G -> numberOfComponents G <= 1

isCyclic = method()
isCyclic Graph := Boolean => G -> isConnected G and all(vertexSet G, v -> degree(G, v) == 2)
isCyclic Digraph := Boolean => G -> (
D := depthFirstSearch G;
any(vertexSet G, u ->
any(toList children(G, u), v ->
(D#symbol discoveryTime)#v < (D#symbol discoveryTime)#u and (D#symbol finishingTime)#u < (D#symbol finishingTime)#v
)
)
)
isCyclic Digraph := Boolean => G -> attemptTopologicalSort(G, identity) === null

isEulerian = method()
isEulerian Graph := Boolean => G -> all(apply(vertexSet G, v -> degree(G,v)), even) and isConnected G
Expand Down Expand Up @@ -5505,6 +5505,17 @@ TEST ///
assert(topologicalSort D==={2,3,1})
///

TEST ///
-- check cycle detection in digraphs
assert( isCyclic digraph({{1,2},{2,3},{3,1}}) === true )
assert( isCyclic digraph({{1,2},{2,3},{3,4},{4,3}}) === true )
assert( isCyclic digraph({{1,2},{2,3},{3,4},{2,4}}) === false )
assert( isCyclic digraph({{1,3},{1,4},{2,4},{3,2},{4,3}}) === true )
assert( isCyclic digraph({{1,3},{1,4}, {3,2},{4,3}}) === false )
assert( isCyclic digraph({{1,2},{2,3},{3,4}}) === false )
assert( isCyclic digraph({{1,2},{2,3},{3,4},{4,4}}) === true )
assert( isCyclic digraph({{1,2},{2,3},{3,4},{5,5}}) === true )
///

TEST ///

Expand Down
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