From a4038e207d4b1b3010f2a6fce80934a794e9845b Mon Sep 17 00:00:00 2001
From: Nenad Ilic <nenadilic84@gmail.com>
Date: Thu, 12 Feb 2026 20:12:11 +0000
Subject: [PATCH 1/2] Add IGraphAlg dispatch for connectivity and
 biconnectivity algorithms

New IGraphAlg methods that dispatch to the igraph C library:

- connected_components: returns component membership as Vector{Vector{Int}}
  matching the Graphs.jl return format
- is_connected: checks weak connectivity via igraph_is_connected
- articulation: finds articulation points via igraph_articulation_points,
  returns sorted 1-based vertex IDs
- bridges: finds bridges via igraph_bridges, converts edge IDs to
  SimpleEdge pairs

All new methods accept any AbstractGraph and convert to IGraph internally,
matching the pattern of the existing diameter/radius/has_isomorph dispatch.

Tests verify output matches Graphs.jl for path, cycle, and disconnected
graphs. All 281 tests pass.
---
 src/graph_api_extensions.jl       | 41 ++++++++++++++++++++++--
 test/test_graph_api_extensions.jl | 53 +++++++++++++++++++++++++++++++
 2 files changed, 92 insertions(+), 2 deletions(-)

diff --git a/src/graph_api_extensions.jl b/src/graph_api_extensions.jl
index ec21b95..2306aa7 100644
--- a/src/graph_api_extensions.jl
+++ b/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
diff --git a/test/test_graph_api_extensions.jl b/test/test_graph_api_extensions.jl
index ea5d600..6fd2ea3 100644
--- a/test/test_graph_api_extensions.jl
+++ b/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

From e5bb5b391c1fb6a5270949222d9be8aa2e6fe4de Mon Sep 17 00:00:00 2001
From: Nenad Ilic <nenadilic84@gmail.com>
Date: Thu, 12 Feb 2026 20:27:11 +0000
Subject: [PATCH 2/2] Update CHANGELOG.md with IGraphAlg dispatch additions

---
 CHANGELOG.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/CHANGELOG.md b/CHANGELOG.md
index 9192490..6a6cde8 100644
--- a/CHANGELOG.md
+++ b/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.