Added clique_number, independence_number

src/Graphs.jl

@@ -314,6 +314,11 @@ export
     triangles,
     label_propagation,
     maximal_cliques,
+    maximum_clique,
+    clique_number,
+    maximal_independent_sets,
+    maximum_independent_set,
+    independence_number,
     clique_percolation,
     assortativity,
     rich_club,

src/community/cliques.jl

@@ -144,3 +144,119 @@ function maximal_cliques end
     end
     return cliques
 end
+
+"""
+    maximum_clique(g)
+
+Return a vector representing the node indices of a maximum clique
+of the undirected graph `g`.
+
+```jldoctest
+julia> using Graphs
+
+julia> maximum_clique(blockdiag(complete_graph(3), complete_graph(4)))
+4-element Vector{Int64}:
+ 4
+ 5
+ 6
+ 7
+```
+"""
+function maximum_clique end
+# see https://github.com/mauro3/SimpleTraits.jl/issues/47#issuecomment-327880153 for syntax
+@traitfn function maximum_clique(g::AG::(!IsDirected)) where {T,AG<:AbstractGraph{T}}
+    return sort(argmax(length, maximal_cliques(g)))
+end
+
+"""
+    clique_number(g)
+
+Returns the size of the largest clique of the undirected graph `g`.
+
+```jldoctest
+julia> using Graphs
+
+julia> clique_number(blockdiag(complete_graph(3), complete_graph(4)))
+4
+```
+"""
+function clique_number end
+# see https://github.com/mauro3/SimpleTraits.jl/issues/47#issuecomment-327880153 for syntax
+@traitfn function clique_number(g::AG::(!IsDirected)) where {T,AG<:AbstractGraph{T}}
+    return maximum(length, maximal_cliques(g))
+end
+
+"""
+    maximal_independent_sets(g)
+
+Return a vector of vectors representing the node indices in each of the maximal
+independent sets found in the undirected graph `g`.
+
+```jldoctest
+julia> using Graphs
+
+julia> maximal_independent_sets(cycle_graph(5))
+5-element Vector{Vector{Int64}}:
+ [5, 2]
+ [5, 3]
+ [2, 4]
+ [1, 4]
+ [1, 3]
+```
+"""
+function maximal_independent_sets end
+# see https://github.com/mauro3/SimpleTraits.jl/issues/47#issuecomment-327880153 for syntax
+@traitfn function maximal_independent_sets(
+    g::AG::(!IsDirected)
+) where {T,AG<:AbstractGraph{T}}
+    # Convert to SimpleGraph first because `complement` doesn't accept AbstractGraph.
+    return maximal_cliques(complement(SimpleGraph(g)))
+end
+
+"""
+    maximum_independent_set(g)
+
+Return a vector representing the node indices of a maximum independent set
+of the undirected graph `g`.
+
+### See also
+[`independent_set`](@ref)
+
+## Examples
+```jldoctest
+julia> using Graphs
+
+julia> maximum_independent_set(cycle_graph(7))
+3-element Vector{Int64}:
+ 2
+ 5
+ 7
+```
+"""
+function maximum_independent_set end
+# see https://github.com/mauro3/SimpleTraits.jl/issues/47#issuecomment-327880153 for syntax
+@traitfn function maximum_independent_set(
+    g::AG::(!IsDirected)
+) where {T,AG<:AbstractGraph{T}}
+    # Convert to SimpleGraph first because `complement` doesn't accept AbstractGraph.
+    return maximum_clique(complement(SimpleGraph(g)))
+end
+
+"""
+    independence_number(g)
+
+Returns the size of the largest independent set of the undirected graph `g`.
+
+```jldoctest
+julia> using Graphs
+
+julia> independence_number(cycle_graph(7))
+3
+```
+"""
+function independence_number end
+# see https://github.com/mauro3/SimpleTraits.jl/issues/47#issuecomment-327880153 for syntax
+@traitfn function independence_number(g::AG::(!IsDirected)) where {T,AG<:AbstractGraph{T}}
+    # Convert to SimpleGraph first because `complement` doesn't accept AbstractGraph.
+    return clique_number(complement(SimpleGraph(g)))
+end

src/independentset/degree_ind_set.jl

@@ -17,6 +17,9 @@ adjacent to the fewest valid vertices in the independent set until all vertices
 ### Performance
 Runtime: O((|V|+|E|)*log(|V|))
 Memory: O(|V|)
+
+### See also
+[`maximum_independent_set`](@ref)
 """
 function independent_set(g::AbstractGraph{T}, alg::DegreeIndependentSet) where {T<:Integer}
     nvg = nv(g)

src/independentset/maximal_ind_set.jl

@@ -20,6 +20,9 @@ Approximation Factor: maximum(degree(g))+1
 ### Optional Arguments
 - `rng=nothing`: set the Random Number Generator.
 - If `seed >= 0`, a random generator is seeded with this value.
+
+### See also
+[`maximum_independent_set`](@ref)
 """
 function independent_set(
     g::AbstractGraph{T},

test/community/cliques.jl

@@ -12,7 +12,12 @@
 
     function test_cliques(graph, expected)
         # Make test results insensitive to ordering
-        return setofsets(@inferred(maximal_cliques(graph))) == setofsets(expected)
+        okay_maximal = setofsets(@inferred(maximal_cliques(graph))) == setofsets(expected)
+        okay_maximum = Set(@inferred(maximum_clique(graph))) in setofsets(expected)
+        okay_maximum2 =
+            length(@inferred(maximum_clique(graph))) == maximum(length.(expected))
+        okay_number = @inferred(clique_number(graph)) == maximum(length.(expected))
+        return okay_maximal && okay_maximum && okay_maximum2 && okay_number
     end
 
     gx = SimpleGraph(3)

test/community/independent_sets.jl

@@ -0,0 +1,34 @@
+##################################################################
+#
+#   Maximal independent sets of undirected graph
+#   Derived from Graphs.jl: https://github.com/julialang/Graphs.jl
+#
+##################################################################
+
+@testset "Independent Sets" begin
+    function setofsets(array_of_arrays)
+        return Set(map(Set, array_of_arrays))
+    end
+
+    function test_independent_sets(graph, expected)
+        # Make test results insensitive to ordering
+        okay_maximal =
+            setofsets(@inferred(maximal_independent_sets(graph))) == setofsets(expected)
+        okay_maximum = Set(@inferred(maximum_independent_set(graph))) in setofsets(expected)
+        okay_maximum2 =
+            length(@inferred(maximum_independent_set(graph))) == maximum(length.(expected))
+        okay_number = @inferred(independence_number(graph)) == maximum(length.(expected))
+        return okay_maximal && okay_maximum && okay_maximum2 && okay_number
+    end
+
+    gx = SimpleGraph(3)
+    add_edge!(gx, 1, 2)
+    for g in test_generic_graphs(gx)
+        @test test_independent_sets(g, Array[[1, 3], [2, 3]])
+    end
+    add_edge!(gx, 2, 3)
+    for g in test_generic_graphs(gx)
+        @test test_independent_sets(g, Array[[1, 3], [2]])
+    end
+    @test independence_number(cycle_graph(11)) == 5
+end

test/runtests.jl

@@ -128,6 +128,7 @@ tests = [
     "traversals/eulerian",
     "community/cliques",
     "community/core-periphery",
+    "community/independent_sets",
     "community/label_propagation",
     "community/modularity",
     "community/clustering",