Add IGraphAlg dispatch for connectivity algorithms

CHANGELOG.md

@@ -1,5 +1,9 @@
 # News
 
+## Unreleased
+
+- Add `IGraphAlg` dispatch for `connected_components`, `is_connected`, `articulation`, and `bridges`.
+
 ## v1.0.0 - 2025-09-25
 
 - Update the underlying igraph C library to v1.0.0.

src/graph_api_extensions.jl

@@ -1,11 +1,12 @@
 # Explicit import/export of the functions
 # that are getting new methods,
 # so that `igraphalg_methods` can pick them up.
-import Graphs: diameter, radius
+import Graphs: diameter, radius, connected_components, is_connected, articulation, bridges
 import Graphs.Experimental
 import Graphs.Experimental: has_isomorph
 
-export diameter, radius, has_isomorph
+export diameter, radius, has_isomorph,
+    connected_components, is_connected, articulation, bridges
 
 struct IGraphAlg end
 
@@ -31,3 +32,39 @@ end
 function has_isomorph(g1, g2, ::IGraphAlg)
     return LibIGraph.isomorphic(IGraph(g1), IGraph(g2))[1]
 end
+
+function connected_components(g, ::IGraphAlg)
+    ig = IGraph(g)
+    membership = IGVectorInt()
+    csize = IGVectorInt()
+    ncomp = LibIGraph.connected_components(ig, membership, csize, LibIGraph.IGRAPH_WEAK)[1]
+    # Convert igraph 0-based component IDs to Graphs.jl format:
+    # Vector of vectors, each containing 1-based vertex IDs
+    components = [Int[] for _ in 1:ncomp]
+    for (v, c) in enumerate(membership)
+        push!(components[c+1], v)
+    end
+    return components
+end
+
+function is_connected(g, ::IGraphAlg)
+    return LibIGraph.is_connected(IGraph(g), LibIGraph.IGRAPH_WEAK)[1]
+end
+
+function articulation(g, ::IGraphAlg)
+    ig = IGraph(g)
+    res = IGVectorInt()
+    LibIGraph.articulation_points(ig, res)
+    return sort!([v + 1 for v in res])
+end
+
+function bridges(g, ::IGraphAlg)
+    ig = IGraph(g)
+    res = IGVectorInt()
+    LibIGraph.bridges(ig, res)
+    # Convert edge IDs to SimpleEdge pairs
+    return [begin
+        (from, to) = LibIGraph.edge(ig, eid)
+        Graphs.SimpleGraphs.SimpleEdge(from+1, to+1)
+    end for eid in res]
+end

test/test_graph_api_extensions.jl

@@ -20,4 +20,57 @@ using Random
     end
 end
 
+@testset "connected_components" begin
+    # Connected graph
+    g = cycle_graph(5)
+    cc = connected_components(g, IGraphAlg())
+    @test length(cc) == 1
+    @test sort(cc[1]) == [1, 2, 3, 4, 5]
+
+    # Disconnected graph: path(3) + isolated vertices
+    g2 = Graph(5)
+    add_edge!(g2, 1, 2)
+    add_edge!(g2, 2, 3)
+    add_edge!(g2, 4, 5)
+    cc2 = connected_components(g2, IGraphAlg())
+    @test length(cc2) == 2
+    cc2_sorted = sort(cc2; by=first)
+    @test sort(cc2_sorted[1]) == [1, 2, 3]
+    @test sort(cc2_sorted[2]) == [4, 5]
+
+    # Match Graphs.jl result (same component grouping)
+    cc_ref = connected_components(g2)
+    @test length(cc2) == length(cc_ref)
+    @test Set(Set.(cc2)) == Set(Set.(cc_ref))
+end
+
+@testset "is_connected" begin
+    @test is_connected(cycle_graph(5), IGraphAlg()) == true
+    g = Graph(4)
+    add_edge!(g, 1, 2)
+    add_edge!(g, 3, 4)
+    @test is_connected(g, IGraphAlg()) == false
+    @test is_connected(g, IGraphAlg()) == is_connected(g)
+end
+
+@testset "articulation" begin
+    g = path_graph(5)
+    art = articulation(g, IGraphAlg())
+    art_ref = sort(articulation(g))
+    @test art == art_ref
+
+    g2 = cycle_graph(5)
+    @test isempty(articulation(g2, IGraphAlg()))
+end
+
+@testset "bridges" begin
+    g = path_graph(5)
+    br = bridges(g, IGraphAlg())
+    br_ref = bridges(g)
+    @test Set(br) == Set(br_ref)
+
+    g2 = cycle_graph(5)
+    @test isempty(bridges(g2, IGraphAlg()))
+end
+
 end