Added clique_number, independence_number

Author: dstahlke

src/Graphs.jl

@@ -120,7 +120,9 @@ barabasi_albert!, static_fitness_model, static_scale_free, kronecker, dorogovtse
 #community
 modularity, core_periphery_deg,
 local_clustering,local_clustering_coefficient, global_clustering_coefficient, triangles,
-label_propagation, maximal_cliques, clique_percolation, assortativity,rich_club,
+maximal_cliques, maximum_clique, clique_number,
+maximal_independent_sets, maximum_independent_set, independence_number,
+label_propagation, clique_percolation, assortativity,rich_club,
 
 #generators
 complete_graph, star_graph, path_graph, wheel_graph, cycle_graph,

src/community/cliques.jl

@@ -137,3 +137,112 @@ 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}}
+    return maximal_cliques(complement(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}}
+    return maximum_clique(complement(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}}
+    return clique_number(complement(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},

src/independentset/maximal_ind_set.jl

@@ -19,6 +19,9 @@ Approximation Factor: maximum(degree(g))+1
 
 ### Optional Arguments
 - 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

@@ -52,4 +52,7 @@
     for g in testgraphs(h)
       @test test_cliques(h, Array[[7, 4, 5], [2, 6], [3, 5], [3, 6], [3, 1]])
     end
+
+    @test clique_number(cycle_graph(11)) == 2
+    @test independence_number(cycle_graph(11)) == 5
 end