ECG Community Detection implementation

CHANGELOG.md

@@ -4,6 +4,7 @@ We follow SemVer as most of the Julia ecosystem. Below you might see the "breaki
 
 ## unreleased
 - `is_articulation(g, v)` for checking whether a single vertex is an articulation point
+- ECG community detection algorithm
 
 
 ## v1.14.0 - 2026-02-26

src/Graphs.jl

@@ -327,6 +327,8 @@ export
     triangles,
     label_propagation,
     louvain,
+    ecg,
+    ecg_weights,
     maximal_cliques,
     maximum_clique,
     clique_number,
@@ -553,6 +555,7 @@ include("centrality/radiality.jl")
 include("community/modularity.jl")
 include("community/label_propagation.jl")
 include("community/louvain.jl")
+include("community/ecg.jl")
 include("community/core-periphery.jl")
 include("community/clustering.jl")
 include("community/cliques.jl")

src/community/ecg.jl

@@ -0,0 +1,136 @@
+"""
+    ecg(g; γ=1, ensemble_size::Integer=16, min_edge_weight=0.05, distmx::AbstractArray{<:Number}=weights(g), max_moves::Integer=1000, max_merges::Integer=1000, move_tol::Real=10e-10, merge_tol::Real=10e-10, rng=nothing, seed=nothing)
+
+Community detection using ensemble clustering for graphs (ECG). Weights the edges based on the
+proportion of time the endpoints are in the same cluster of a Louvain without merges before running
+a final Louvain to detect communities.
+
+### Optional Arguments
+- `distmx=weights(g)`: distance matrix for weighted graphs
+- `ensemble_size=16`: the number of no merge Louvains in the ensemble
+- `min_edge_weight`: the minimum edge weight passed to the final Louvain (to retain the original topology).
+- `γ=1.0`: where `γ > 0` is a resolution parameter. Higher resolutions lead to more
+    communities, while lower resolutions lead to fewer communities. Where `γ=1.0` it
+    leads to the traditional definition of the modularity.
+- `max_moves=1000`: maximum number of rounds moving vertices before merging for each Louvain.
+- `max_merges=1000`: maximum number of merges in the final Louvain.
+- `move_tol=10e-10`: necessary increase of modularity to move a vertex in each Louvain.
+- `merge_tol=10e-10`: necessary increase of modularity in the move stage to merge in the final Louvain.
+- `rng=nothing`: rng to use for reproducibility. May only pass one of rng or seed.
+- `seed=nothing`: seed to use for reproducibility. May only pass one of rng or seed.
+
+### References
+- [Valérie Poulin and François Théberge. Ensemble Clustering for Graphs: Comparisons and Applications. Applied Network Science, 4:4 (2019)][https://doi.org/10.1007/s41109-019-0162-z]
+
+
+# Examples 
+```jldoctest
+julia> using Graphs
+
+julia> barbell = blockdiag(complete_graph(3), complete_graph(3));
+
+julia> add_edge!(barbell, 1, 4);
+
+julia> ecg(barbell)
+6-element Vector{Int64}:
+ 1
+ 1
+ 1
+ 2
+ 2
+ 2
+
+julia> ecg(barbell, γ=0.01)
+6-element Vector{Int64}:
+ 1
+ 1
+ 1
+ 1
+ 1
+ 1
+```
+"""
+function ecg(
+    g::AbstractGraph{T};
+    γ=1.0,
+    ensemble_size::Integer=16,
+    min_edge_weight::Real=0.05,
+    distmx::AbstractArray{<:Number}=weights(g),
+    max_moves::Integer=1000,
+    max_merges::Integer=1000,
+    move_tol::Real=10e-10,
+    merge_tol::Real=10e-10,
+    rng::Union{Nothing,AbstractRNG}=nothing,
+    seed::Union{Nothing,Integer}=nothing,
+) where {T}
+    rng = rng_from_rng_or_seed(rng, seed)
+    if nv(g) == 0
+        return T[]
+    end
+    ensemble_weights = ecg_weights(
+        g;
+        γ=γ,
+        ensemble_size=ensemble_size,
+        distmx=distmx,
+        max_moves=max_moves,
+        move_tol=move_tol,
+        rng=rng,
+    )
+    weights =
+        (1-min_edge_weight)*ensemble_weights +
+        min_edge_weight * adjacency_matrix(g, Float64)
+    return louvain(
+        g;
+        γ=γ,
+        distmx=weights,
+        max_moves=max_moves,
+        max_merges=max_merges,
+        move_tol=move_tol,
+        merge_tol=merge_tol,
+        rng=rng,
+    )
+end
+
+"""
+    ensemble_weights(g; c, distmx, max_moves, move_tol, rng, seed)
+
+Compute edge weights via an ensemble of no merge Louvains. The weight of each edge is
+the proportion of time the endpoints are in the same community. 
+"""
+function ecg_weights(
+    g::AbstractGraph{T};
+    γ=1.0,
+    ensemble_size::Integer=16,
+    distmx::AbstractArray{<:Number}=weights(g),
+    max_moves::Integer=1000,
+    move_tol::Real=10e-10,
+    rng::Union{Nothing,AbstractRNG}=nothing,
+    seed::Union{Nothing,Integer}=nothing,
+) where {T}
+    rng = rng_from_rng_or_seed(rng, seed)
+    # Create sparse adjacency matrix full of explicit zeros
+    ensemble_weights = adjacency_matrix(g, Float64)
+    ensemble_weights.nzval .= 0
+
+    for _ in 1:ensemble_size
+        ensemble_communities = louvain(
+            g;
+            γ=γ,
+            distmx=distmx,
+            max_moves=max_moves,
+            max_merges=0,
+            move_tol=move_tol,
+            rng=rng,
+        )
+        for e in edges(g)
+            if ensemble_communities[src(e)] == ensemble_communities[dst(e)]
+                ensemble_weights[src(e), dst(e)] += 1 / ensemble_size
+                if !is_directed(g)
+                    ensemble_weights[dst(e), src(e)] += 1 / ensemble_size
+                end
+            end
+        end
+    end
+
+    return ensemble_weights
+end

test/community/ecg.jl

@@ -0,0 +1,129 @@
+@testset "ECG" begin
+    # Test ecg_weights
+    # Undirected
+    barbell = barbell_graph(3, 3)
+    c = sparse(
+        [
+            0.0 1.0 1.0 0.0 0.0 0.0;
+            1.0 0.0 1.0 0.0 0.0 0.0;
+            1.0 1.0 0.0 0.0 0.0 0.0;
+            0.0 0.0 0.0 0.0 1.0 1.0;
+            0.0 0.0 0.0 1.0 0.0 1.0;
+            0.0 0.0 0.0 1.0 1.0 0.0
+        ],
+    )
+    for g in test_generic_graphs(barbell)
+        r = ecg_weights(g)
+        dropzeros!(r)
+        @test c == r
+    end
+
+    # Empty, no edges
+    empty = SimpleGraph(10)
+    c = spzeros(10, 10)
+    for g in test_generic_graphs(empty)
+        r = @inferred ecg_weights(g)
+        dropzeros!(r)
+        @test c == r
+    end
+
+    # Empty, no nodes
+    empty = SimpleGraph()
+    c = spzeros(0, 0)
+    for g in test_generic_graphs(empty)
+        r = @inferred ecg_weights(g)
+        @test c == r
+    end
+
+    # Undirected loops
+    loops = complete_graph(2)
+    add_edge!(loops, 1, 1)
+    add_edge!(loops, 2, 2)
+    c = sparse([
+        2.0 0.0;
+        0.0 2.0
+    ])
+    for g in test_generic_graphs(loops)
+        r = ecg_weights(g)
+        dropzeros!(r)
+        @test c == r
+    end
+
+    # Directed
+    triangle = SimpleDiGraph(3)
+    add_edge!(triangle, 1, 2)
+    add_edge!(triangle, 2, 3)
+    add_edge!(triangle, 3, 1)
+
+    # Directed Loops
+    barbell = blockdiag(triangle, triangle)
+    add_edge!(barbell, 1, 4)
+    c = sparse(
+        [
+            0.0 1.0 0.0 0.0 0.0 0.0;
+            0.0 0.0 1.0 0.0 0.0 0.0;
+            1.0 0.0 0.0 0.0 0.0 0.0;
+            0.0 0.0 0.0 0.0 1.0 0.0;
+            0.0 0.0 0.0 0.0 0.0 1.0;
+            0.0 0.0 0.0 1.0 0.0 0.0
+        ],
+    )
+    for g in test_generic_graphs(barbell)
+        r = ecg_weights(g)
+        dropzeros!(r)
+        @test r == c
+    end
+
+    # Directed loops
+    barbell = SimpleDiGraph(2)
+    add_edge!(barbell, 1, 1)
+    add_edge!(barbell, 2, 2)
+    add_edge!(barbell, 1, 2)
+    c = sparse([
+        1.0 0.0;
+        0.0 1.0
+    ])
+    for g in test_generic_graphs(barbell)
+        r = ecg_weights(g)
+        dropzeros!(r)
+        @test r == c
+    end
+
+    # Test ECG
+    # Undirected
+    barbell = barbell_graph(3, 3)
+    c = [1, 1, 1, 2, 2, 2]
+    for g in test_generic_graphs(barbell)
+        r = ecg(g)
+        @test c == r
+    end
+
+    # Directed
+    triangle = SimpleDiGraph(3)
+    add_edge!(triangle, 1, 2)
+    add_edge!(triangle, 2, 3)
+    add_edge!(triangle, 3, 1)
+
+    barbell = blockdiag(triangle, triangle)
+    add_edge!(barbell, 1, 4)
+    c = [1, 1, 1, 2, 2, 2]
+    for g in test_generic_graphs(barbell)
+        r = ecg(g)
+        @test r == c
+    end
+
+    # Empty, no edges
+    empty = SimpleGraph(10)
+    c = collect(1:10)
+    for g in test_generic_graphs(empty)
+        r = ecg(g)
+        @test c == r
+    end
+
+    # Empty, no nodes
+    empty = SimpleGraph()
+    for g in test_generic_graphs(empty)
+        r = ecg(g)
+        @test length(r) == 0
+    end
+end

test/runtests.jl

@@ -118,6 +118,7 @@ tests = [
     "traversals/all_simple_paths",
     "community/cliques",
     "community/core-periphery",
+    "community/ecg",
     "community/independent_sets",
     "community/label_propagation",
     "community/louvain",