Eulerian paths

src/lib/GraphsExtensions/src/GraphsExtensions.jl

@@ -6,6 +6,7 @@ include("neighbors.jl")
 include("shortestpaths.jl")
 include("symrcm.jl")
 include("partitioning.jl")
+include("traversal.jl")
 include("trees_and_forests.jl")
 include("simplegraph.jl")
 end

src/lib/GraphsExtensions/src/traversal.jl

@@ -0,0 +1,42 @@
+
+#Given a graph, traverse it from start vertex to end vertex, covering each edge exactly once.
+#Complexity is O(length(edges(g)))
+function eulerian_path(g::AbstractGraph, start_vertex, end_vertex)
+  #Conditions on g for the required path to exist
+  if start_vertex != end_vertex
+    @assert isodd(degree(g, start_vertex) % 2)
+    @assert isodd(degree(g, end_vertex) % 2)
+    @assert all(
+      x -> iseven(x), degrees(g, setdiff(vertices(g), [start_vertex, end_vertex]))
+    )
+  else
+    @assert all(x -> iseven(x), degrees(g, vertices(g)))
+  end
+
+  path = []
+  stack = []
+  current_vertex = end_vertex
+  g_modified = copy(g)
+  while !isempty(stack) || !iszero(degree(g_modified, current_vertex))
+    if iszero(degree(g_modified, current_vertex))
+      append!(path, current_vertex)
+      last_vertex = pop!(stack)
+      current_vertex = last_vertex
+    else
+      append!(stack, current_vertex)
+      vn = first(neighbors(g_modified, current_vertex))
+      rem_edge!(g_modified, edgetype(g_modified)(current_vertex, vn))
+      current_vertex = vn
+    end
+  end
+
+  append!(path, current_vertex)
+
+  return edgetype(g_modified)[
+    edgetype(g_modified)(path[i], path[i + 1]) for i in 1:(length(path) - 1)
+  ]
+end
+
+function eulerian_cycle(g::AbstractGraph, start_vertex)
+  return eulerian_path(g, start_vertex, start_vertex)
+end

src/lib/GraphsExtensions/test/runtests.jl

@@ -52,6 +52,9 @@ using NamedGraphs.GraphsExtensions:
   directed_graph_type,
   disjoint_union,
   distance_to_leaves,
+  _eulerian_cycle,
+  eulerian_cycle,
+  eulerian_path,
   has_edges,
   has_leaf_neighbor,
   has_vertices,
@@ -68,6 +71,7 @@ using NamedGraphs.GraphsExtensions:
   is_rooted,
   is_self_loop,
   leaf_vertices,
+  make_all_degrees_even,
   minimum_distance_to_leaves,
   next_nearest_neighbors,
   non_leaf_edges,
@@ -588,5 +592,15 @@ using Test: @test, @test_broken, @test_throws, @testset
   @test only(vertices_at_distance(g, 1, L - 1)) == L
   @test only(next_nearest_neighbors(g, 1)) == 3
   @test issetequal(vertices_at_distance(g, 5, 3), [2, 8])
+
+  #Eulerian paths
+  g = path_graph(L)
+  path = eulerian_path(g, 1, L)
+  @test path == [edgetype(g)(i, i + 1) for i in 1:(L - 1)]
+
+  g = add_edge(g, L => 1)
+  cycle = eulerian_cycle(g, 1)
+  correct_cycle = vcat([edgetype(g)(i, i + 1) for i in 1:(L - 1)], [edgetype(g)(L, 1)])
+  @test cycle == correct_cycle || reverse(reverse.(cycle)) == correct_cycle
 end
 end