Create induced subgraph from edge list (#37)

In order to fix
[#32](#32),
I have added an implementation of the `induced_subgraph` function that
creates an edge induced subgraph from a list of edges.

---------

Co-authored-by: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>

Author: pgrepds

Project.toml

@@ -19,7 +19,8 @@ Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
 JuliaFormatter = "98e50ef6-434e-11e9-1051-2b60c6c9e899"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Aqua", "Documenter", "Graphs", "JuliaFormatter", "LinearAlgebra", "Test"]
+test = ["Aqua", "Documenter", "Graphs", "JuliaFormatter", "LinearAlgebra", "SparseArrays", "Test"]

src/overrides.jl

@@ -162,12 +162,50 @@ Compute the weighted subgraph induced by a list of vertices.
 Return a tuple containing the new graph and the list of vertices.
 """
 function Graphs.induced_subgraph(
-    g::T, vlist::AbstractVector{U}
-) where {T<:AbstractSimpleWeightedGraph,U<:Integer}
-    E = eltype(g)
+    g::G, vlist::AbstractVector{U}
+) where {G<:AbstractSimpleWeightedGraph,U<:Integer}
+    T = eltype(g)
     allunique(vlist) || throw(ArgumentError("Vertices in subgraph list must be unique"))
-    new_weights = g.weights[E.(vlist), E.(vlist)]
+    new_weights = g.weights[T.(vlist), T.(vlist)]
     newg = zero(g)
     newg.weights = new_weights
-    return newg, Vector{E}(vlist)
+    return newg, Vector{T}(vlist)
+end
+
+function Graphs.induced_subgraph(
+    g::G, elist::AbstractVector{E}
+) where {G<:AbstractSimpleWeightedGraph} where {E<:AbstractEdge}
+    allunique(elist) || throw(ArgumentError("Edges in subgraph list must be unique"))
+    T, U = eltype(g), weighttype(g)
+    vertex_set = Set{T}()
+    for e in elist
+        if has_edge(g, e)
+            push!(vertex_set, src(e), dst(e))
+        else
+            @warn "Skipping the edge $(e), since it does not exist in the graph!"
+        end
+    end
+    vertex_list = collect(vertex_set)
+    sort!(vertex_list)
+    index_map = Dict(vertex_list[i] => i for i in eachindex(vertex_list))
+    n = length(vertex_list)
+    new_weights = spzeros(weighttype(g), T, n, n)
+    I, J, W = T[], T[], U[]
+    for e in elist
+        if has_edge(g, e)
+            i, j = index_map[src(e)], index_map[dst(e)]
+            w = get_weight(g, dst(e), src(e))
+            push!(I, j)  # storage is transposed!
+            push!(J, i)
+            push!(W, w)
+            if !is_directed(g)
+                push!(I, i)
+                push!(J, j)
+                push!(W, w)
+            end
+        end
+    end
+    new_weights = sparse(I, J, W)
+    newg = G(new_weights)
+    return newg, vertex_list
 end

test/simpleweightedgraph.jl

@@ -1,4 +1,5 @@
 using SimpleWeightedGraphs
+using SparseArrays
 
 @testset verbose = true "SimpleWeightedGraphs" begin
     @info("Ignore warnings relating to adding and removing vertices and edges")
@@ -351,4 +352,33 @@ using SimpleWeightedGraphs
         @test g[1, 3, Val{:weight}()] ≈ 0
         @test g[2, 3, Val{:weight}()] ≈ 0.5
     end
+
+    # this testset was implemented for https://github.com/JuliaGraphs/SimpleWeightedGraphs.jl/issues/32
+    @testset "induced_subgraph should preserve weights for edge lists" begin
+        g = SimpleWeightedGraph([0 2; 2 0])
+        expected_graph_weights = sparse([0 2; 2 0])
+        # vertex induced subgraph
+        vertex_induced_subgraph_weights = weights(first(induced_subgraph(g, [1, 2])))
+        @test vertex_induced_subgraph_weights == expected_graph_weights
+        # edge induced subgraph
+        edge_induced_subgraph_weights = weights(first(induced_subgraph(g, [Edge(1, 2)])))
+        @test edge_induced_subgraph_weights == expected_graph_weights
+
+        # test edge induced graph with one edge removed
+        # graph isomorphic to C_5
+        g = SimpleWeightedGraph([0 2 0 0 2; 2 0 2 0 0; 0 2 0 2 0; 0 0 2 0 2; 2 0 0 2 0])
+        expected_graph_weights = sparse(
+            [0 2 0 0 0; 2 0 2 0 0; 0 2 0 2 0; 0 0 2 0 2; 0 0 0 2 0]
+        )
+        # create edge induced subgraph isomorphic to P_5. The edge (1, 5) is missing and test if weights are correct.
+        edge_induced_subgraph_weights = weights(
+            first(induced_subgraph(g, [Edge(1, 2), Edge(2, 3), Edge(3, 4), Edge(4, 5)]))
+        )
+        @test edge_induced_subgraph_weights == expected_graph_weights
+
+        # test edge induced subgraph which does not contain the whole vertex set, especially remove the first column (vertex 1)
+        edge_induced_subgraph_weights = weights(first(induced_subgraph(g, [Edge(2, 3)])))
+        expected_graph_weights = sparse([0 2; 2 0])
+        @test edge_induced_subgraph_weights == expected_graph_weights
+    end
 end