fix is_cyclic (#168)

* fix is_cyclic

* fix unconnected graphs

* fixed graph for test

* better performance with dfs

* new version

* test inferred corrected

Co-authored-by: Lionel Zoubritzky <Liozou@users.noreply.github.com>

* removed empty line

Co-authored-by: Lionel Zoubritzky <Liozou@users.noreply.github.com>

* better style in push

Co-authored-by: Lionel Zoubritzky <Liozou@users.noreply.github.com>

* vector improved

Co-authored-by: Lionel Zoubritzky <Liozou@users.noreply.github.com>

* update parent

Co-authored-by: Lionel Zoubritzky <Liozou@users.noreply.github.com>

* Update src/traversals/dfs.jl

Co-authored-by: Lionel Zoubritzky <Liozou@users.noreply.github.com>

* spaces

Co-authored-by: Lionel Zoubritzky <Liozou@users.noreply.github.com>

* Update src/traversals/dfs.jl

Co-authored-by: Lionel Zoubritzky <Liozou@users.noreply.github.com>

* new version thanks to @Liozou

* fixed tests and documentation self-loops

* self loops undirected

* Update src/traversals/dfs.jl

Co-authored-by: Simon Schölly <sischoel@gmail.com>

Co-authored-by: Lionel Zoubritzky <Liozou@users.noreply.github.com>
Co-authored-by: Simon Schölly <sischoel@gmail.com>

Author: 3 people

src/traversals/dfs.jl

@@ -7,10 +7,29 @@
 Return `true` if graph `g` contains a cycle.
 
 ### Implementation Notes
-Uses DFS.
+The algorithm uses a DFS. Self-loops are counted as cycles.
 """
 function is_cyclic end
-@traitfn is_cyclic(g::::(!IsDirected)) = ne(g) > 0
+@enum Vertex_state unvisited visited
+@traitfn function is_cyclic(g::AG::(!IsDirected)) where {T, AG<:AbstractGraph{T}}
+    visited = falses(nv(g)) 
+    for v in vertices(g)
+        visited[v] && continue
+        visited[v] = true
+        S = [(v,v)] 
+        while !isempty(S)
+            parent, w = pop!(S)
+            for u in neighbors(g, w)
+                u == w && return true # self-loop
+                u == parent && continue
+                visited[u] && return true
+                visited[u] = true
+                push!(S, (w, u))
+            end
+        end
+    end
+    return false
+end
 # see https://github.com/mauro3/SimpleTraits.jl/issues/47#issuecomment-327880153 for syntax
 @traitfn function is_cyclic(g::AG::IsDirected) where {T, AG<:AbstractGraph{T}}
     vcolor = zeros(UInt8, nv(g))

test/traversals/dfs.jl

@@ -1,9 +1,15 @@
 @testset "DFS" begin
-
+  gnodes_directed=SimpleDiGraph(4)
+  gnodes_undirected=SimpleGraph(4)
+  gloop_directed=SimpleDiGraph(1)
+  add_edge!(gloop_directed, 1, 1);
+  gloop_undirected=SimpleGraph(1)
+  add_edge!(gloop_undirected, 1, 1);
   g5 = SimpleDiGraph(4)
   add_edge!(g5, 1, 2); add_edge!(g5, 2, 3); add_edge!(g5, 1, 3); add_edge!(g5, 3, 4)
   gx = cycle_digraph(3)
-
+  gcyclic = SimpleGraph([0 1 1 0 0; 1 0 1 0 0; 1 1 0 0 0; 0 0 0 0 1; 0 0 0 1 0])
+  gtree = SimpleGraph([0 1 1 1 0 0 0; 1 0 0 0 0 0 0; 1 0 0 0 0 0 0; 1 0 0 0 1 1 1; 0 0 0 1 0 0 0; 0 0 0 1 0 0 0; 0 0 0 1 0 0 0])
   @testset "dfs_tree" begin
     for g in testdigraphs(g5)
       z = @inferred(dfs_tree(g, 1))
@@ -26,8 +32,29 @@
 
   @testset "is_cyclic" begin
     for g in testgraphs(path_graph(2))
+      @test !@inferred(is_cyclic(g))
+      @test !@inferred(is_cyclic(zero(g)))
+    end
+    for g in testgraphs(gcyclic)
+      @test @inferred(is_cyclic(g))
+    end
+    for g in testgraphs(gtree)
+      @test !@inferred(is_cyclic(g))
+    end
+    for g in testgraphs(g5)
+      @test !@inferred(is_cyclic(g))
+    end
+    for g in testgraphs(gnodes_directed)
+      @test !@inferred(is_cyclic(g))
+    end
+    for g in testgraphs(gnodes_undirected)
+      @test !@inferred(is_cyclic(g))
+    end
+    for g in testgraphs(gloop_directed)
+      @test @inferred(is_cyclic(g))
+    end
+    for g in testgraphs(gloop_undirected)
       @test @inferred(is_cyclic(g))
-      @test @inferred(!is_cyclic(zero(g)))
     end
   end