Add/line graph

.gitignore

@@ -14,3 +14,4 @@ benchmark/Manifest.toml
 /docs/src/index.md
 /docs/src/contributing.md
 /docs/src/license.md
+.aider*

src/Graphs.jl

@@ -165,6 +165,7 @@ export
     egonet,
     merge_vertices!,
     merge_vertices,
+    line_graph,
 
     # bfs
     gdistances,

src/operators.jl

@@ -879,3 +879,88 @@ function merge_vertices!(g::Graph{T}, vs::Vector{U} where {U<:Integer}) where {T
 
     return new_vertex_ids
 end
+
+"""
+	line_graph(g::SimpleGraph)
+Given a graph `g`, return the graph `lg`, whose vertices are integers that enumerate the 
+edges in `g`, and two vertices in `lg` form an edge iff the corresponding edges in `g` 
+share a common endpoint. In other words, edges in `lg` are length-2 paths in `g`. 
+Note that `i ∈ vertices(lg)` corresponds to `collect(edges(g))[i]`. 
+
+# Examples
+```jldoctest
+julia> using Graphs
+
+julia> g = path_graph(5);
+
+julia> lg = line_graph(g)
+{4, 3} undirected simple Int64 graph
+```
+"""
+function line_graph(g::SimpleGraph)::SimpleGraph
+    vertex_to_edges = [Int[] for _ in 1:nv(g)]
+    for (i, e) in enumerate(edges(g))
+        s, d = src(e), dst(e)
+        push!(vertex_to_edges[s], i)
+        s == d && continue  # do not push self-loops twice
+        push!(vertex_to_edges[d], i)
+    end
+
+    edge_to_neighbors = [Int[] for _ in 1:ne(g)]
+    m = 0  # number of edges in the line-graph
+    for es in vertex_to_edges
+        n = length(es)
+        for i in 1:(n - 1), j in (i + 1):n  # iterate through pairs of edges with same endpoint
+            ei, ej = es[i], es[j]
+            m += 1
+            push!(edge_to_neighbors[ei], ej)
+            push!(edge_to_neighbors[ej], ei)
+        end
+    end
+
+    foreach(sort!, edge_to_neighbors)
+    return SimpleGraph(m, edge_to_neighbors)
+end
+
+"""
+	line_graph(g::SimpleDiGraph)
+Given a digraph `g`, return the digraph `lg`, whose vertices are integers that enumerate 
+the edges in `g`, and there is an edge in `lg` from `Edge(a,b)` to `Edge(c,d)` iff b==c.
+In other words, edges in `lg` are length-2 directed paths in `g`. 
+Note that `i ∈ vertices(lg)` corresponds to `collect(edges(g))[i]`. 
+
+# Examples
+```jldoctest
+julia> using Graphs
+
+julia> g = cycle_digraph(5);
+
+julia> lg = line_graph(g)
+{5, 5} directed simple Int64 graph
+```
+"""
+function line_graph(g::SimpleDiGraph)::SimpleDiGraph
+    vertex_to_edgesout = [Int[] for _ in 1:nv(g)]
+    vertex_to_edgesin = [Int[] for _ in 1:nv(g)]
+    for (i, e) in enumerate(edges(g))
+        s, d = src(e), dst(e)
+        push!(vertex_to_edgesout[s], i)
+        push!(vertex_to_edgesin[d], i)
+    end
+
+    edge_to_neighborsout = [Int[] for _ in 1:ne(g)]
+    edge_to_neighborsin = [Int[] for _ in 1:ne(g)]
+    m = 0  # number of edges in the line-graph
+    for (e_i, e_o) in zip(vertex_to_edgesin, vertex_to_edgesout)
+        for ei in e_i, eo in e_o  # iterate through length-2 directed paths
+            ei == eo && continue  # a self-loop in g does not induce a self-loop in lg
+            m += 1
+            push!(edge_to_neighborsout[ei], eo)
+            push!(edge_to_neighborsin[eo], ei)
+        end
+    end
+
+    foreach(sort!, edge_to_neighborsout)
+    foreach(sort!, edge_to_neighborsin)
+    return SimpleDiGraph(m, edge_to_neighborsout, edge_to_neighborsin)
+end

test/operators.jl

@@ -352,4 +352,96 @@
     @testset "Length: $(typeof(g))" for g in test_generic_graphs(SimpleGraph(100))
         @test length(g) == 10000
     end
+
+    @testset "Undirected Line Graph" begin
+        @testset "Undirected Cycle Graphs" begin
+            for n in 3:9
+                g = cycle_graph(n)
+                lg = line_graph(g)  # checking if lg is an n-cycle
+                @test nv(lg) == n
+                @test ne(lg) == n
+                @test is_connected(lg)
+                @test all(degree(lg, v) == 2 for v in vertices(lg))
+            end
+        end
+
+        @testset "Undirected Path Graphs" begin
+            for n in 2:9
+                g = path_graph(n)
+                lg = line_graph(g)  # checking if lg is an n-1-path
+                @test nv(lg) == n - 1
+                @test ne(lg) == n - 2
+                @test is_connected(lg)
+                @test all(degree(lg, v) <= 2 for v in vertices(lg))
+                @test any(degree(lg, v) == 1 for v in vertices(lg)) || n == 2 && ne(lg) == 0
+            end
+        end
+
+        @testset "Undirected Star Graphs" begin
+            for n in 3:9
+                g = star_graph(n)
+                lg = line_graph(g)  # checking if lg is a complete graph on n-1 vertices
+                @test nv(lg) == n - 1
+                @test ne(lg) == binomial(n - 1, 2)  # lg must be a complete graph
+            end
+        end
+
+        @testset "Undirected Self-loops" begin
+            g = SimpleGraph(2, [[2], [1, 2], Int[]])
+            lg = line_graph(g)
+            @test nv(lg) == 2  # only 2 edges (self-loop counts once)                                                                                                                                                                           
+            @test ne(lg) == 1  # only connection between edge 1-2 and self-loop 2-2                                                                                                                                                               
+        end
+    end
+
+    @testset "Directed Line Graph" begin
+        @testset "Directed Cycle Graphs" begin
+            for n in 3:9
+                g = cycle_digraph(n)
+                lg = line_graph(g)
+                @test nv(lg) == n
+                @test ne(lg) == n
+                @test is_directed(lg)
+                @test is_connected(lg)
+                @test all(outdegree(lg, v) == 1 for v in vertices(lg))
+                @test all(indegree(lg, v) == 1 for v in vertices(lg))
+            end
+        end
+
+        @testset "Directed Path Graphs" begin
+            for n in 2:9
+                g = path_digraph(n)
+                lg = line_graph(g)
+                @test nv(lg) == n - 1
+                @test ne(lg) == n - 2
+                @test is_directed(lg)
+                @test is_connected(lg)
+                @test all(outdegree(lg, v) == (v < n - 1 ? 1 : 0) for v in vertices(lg))
+                @test all(indegree(lg, v) == (v > 1 ? 1 : 0) for v in vertices(lg))
+            end
+        end
+
+        @testset "Directed Star Graphs" begin
+            for m in 0:4, n in 0:4
+                g = SimpleDiGraph(m + n + 1)
+                foreach(i -> add_edge!(g, i + 1, 1), 1:m)
+                foreach(j -> add_edge!(g, 1, j + 1 + m), 1:n)
+                lg = line_graph(g)  # checking if lg is the complete bipartite digraph
+                @test nv(lg) == m + n
+                @test ne(lg) == m * n
+                @test all(outdegree(lg, v) == 0 && indegree(lg, v) == m for v in 1:n)
+                @test all(
+                    outdegree(lg, v) == n && indegree(lg, v) == 0 for v in (n + 1):(n + m)
+                )
+            end
+        end
+
+        @testset "Directed Self-loops" begin
+            g = SimpleDiGraph(2, [[1, 2], Int[], Int[]], [[1], [1], Int[]])
+            lg = line_graph(g)
+            @test nv(lg) == 2
+            @test ne(lg) == 1
+            @test has_edge(lg, 1, 2)
+        end
+    end
 end

test/runtests.jl

@@ -1,11 +1,11 @@
 using Aqua
 using Documenter
 using Graphs
-using Graphs.SimpleGraphs
 using Graphs.Experimental
+using Graphs.SimpleGraphs
+using Graphs.Test
 using JET
 using JuliaFormatter
-using Graphs.Test
 using Test
 using SparseArrays
 using LinearAlgebra
@@ -150,31 +150,42 @@ tests = [
     "experimental/experimental",
 ]
 
+args = lowercase.(ARGS)
+
 @testset verbose = true "Graphs" begin
-    @testset "Code quality (JET.jl)" begin
-        @assert get_pkg_version("JET") >= v"0.8.4"
-        JET.test_package(
-            Graphs;
-            target_defined_modules=true,
-            ignore_missing_comparison=true,
-            mode=:typo,  # TODO: switch back to `:basic` once the union split caused by traits is fixed
-        )
+    if "jet" in args || isempty(args)
+        @testset "Code quality (JET.jl)" begin
+            @assert get_pkg_version("JET") >= v"0.8.4"
+            JET.test_package(
+                Graphs;
+                target_defined_modules=true,
+                ignore_missing_comparison=true,
+                mode=:typo,  # TODO: switch back to `:basic` once the union split caused by traits is fixed
+            )
+        end
     end
 
-    @testset "Code quality (Aqua.jl)" begin
-        Aqua.test_all(Graphs; ambiguities=false)
+    if "aqua" in args || isempty(args)
+        @testset "Code quality (Aqua.jl)" begin
+            Aqua.test_all(Graphs; ambiguities=false)
+        end
     end
 
-    @testset "Code formatting (JuliaFormatter.jl)" begin
-        @test format(Graphs; verbose=false, overwrite=false)
+    if "juliaformatter" in args || isempty(args)
+        @testset "Code formatting (JuliaFormatter.jl)" begin
+            @test format(Graphs; verbose=false, overwrite=false)
+        end
     end
 
-    doctest(Graphs)
+    if "doctest" in args || isempty(args)
+        doctest(Graphs)
+    end
 
     @testset verbose = true "Actual tests" begin
         for t in tests
-            tp = joinpath(testdir, "$(t).jl")
-            include(tp)
+            if t in args || isempty(args)
+                include(joinpath(testdir, "$(t).jl"))
+            end
         end
     end
 end;