Add overlapping communities functionality

Manifest.toml

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src/ABCDGraphGenerator.jl

@@ -5,6 +5,7 @@ using StatsBase
 using ArgParse
 
 include("pl_sampler.jl")
+include("community_sampler.jl")
 include("graph_sampler.jl")
 
 end # module

src/community_sampler.jl

@@ -0,0 +1,73 @@
+using Random
+using StatsBase
+
+function sample_points(n)
+    points = randn(n, 2)
+    points ./= sqrt.(sum(x -> x^2, points, dims=2))
+    points .*= rand(n) .^ 0.5
+    return points
+end
+
+function assign_points(x, c, p)
+    @assert ndims(x) == 2
+    @assert sum(c) == size(x, 1)
+    @assert length(c) == length(p)
+    x = copy(x)
+    all_idxs = collect(1:size(x, 1))
+    dist = vec(sum(x -> x^2, x, dims=2))
+    res = Vector{Vector{Int}}(UndefInitializer(), length(c))
+    for idx in p
+        com = c[idx]
+        ind = argmax(dist)
+        ref = x[ind, :]
+        dist_c = [sum(x -> x^2, (r - ref)) for r in eachrow(x)]
+        idxs = partialsortperm(dist_c, 1:com)
+        res[idx] = all_idxs[idxs]
+        to_keep = setdiff(1:size(x, 1), idxs)
+        x = x[to_keep, :]
+        dist = dist[to_keep]
+        all_idxs = all_idxs[to_keep]
+    end
+    @assert size(x, 1) == 0
+    @assert length(all_idxs) == 0
+    @assert length(dist) == 0
+    @assert sort(union(res...)) == 1:sum(c)
+    return res
+end
+
+# note that this function returns node numbers from 1 to number_of_non_outlier_nodes
+# for each community we get a set of nodes assigned to it
+function populate_overlapping_clusters(coms::Vector{Int}, η::Float64)
+    true_coms = coms[2:end] # we are interested only in non-outlier communities
+    grow_coms = [randround(s * η) for s in true_coms] # this is a target size of communities, as coms is primary community sizes
+    p = randperm(length(true_coms)) # order in which communities are handled
+    n = sum(true_coms)
+    x = sample_points(n)
+    a = assign_points(x, true_coms, p)
+    @assert length.(a) == true_coms
+    @assert sum(length, a) == sum(true_coms)
+
+    # below we grow communities
+    @assert length(a) == length(grow_coms)
+    for (com, target) in zip(a, grow_coms)
+        community_center = vec(mean(x[com], dims=1))
+        distances = [sum((v .- community_center) .^ 2) for v in eachrow(x)]
+        ordering = sortperm(distances)
+        com_set = Set(com)
+        loc = 1
+        while length(com) < target
+            if loc > length(ordering)
+                throw(ArgumentError("η was too large"))
+            end
+            point = ordering[loc]
+            if !(point in com_set)
+                push!(com, point)
+            end
+            loc += 1
+        end
+    end
+    @assert length.(a) == grow_coms
+    @assert sum(length, a) == sum(grow_coms)
+    @assert all(allunique(c) for c in a)
+    return [Set(c) for c in a]
+end