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// SPDX-License-Identifier: Apache-2.0
// Copyright 2024-2026 Dragonscale Team
//! Louvain Community Detection Algorithm.
use crate::algo::GraphProjection;
use crate::algo::algorithms::Algorithm;
use std::collections::HashMap;
use uni_common::core::id::Vid;
pub struct Louvain;
#[derive(Debug, Clone)]
pub struct LouvainConfig {
pub resolution: f64,
pub max_iterations: usize,
pub min_modularity_gain: f64,
}
impl Default for LouvainConfig {
fn default() -> Self {
Self {
resolution: 1.0,
max_iterations: 10,
min_modularity_gain: 1e-4,
}
}
}
pub struct LouvainResult {
pub communities: Vec<(Vid, u64)>,
pub modularity: f64,
pub community_count: usize,
}
impl Algorithm for Louvain {
type Config = LouvainConfig;
type Result = LouvainResult;
fn name() -> &'static str {
"louvain"
}
fn run(graph: &GraphProjection, config: Self::Config) -> Self::Result {
let n = graph.vertex_count();
if n == 0 {
return LouvainResult {
communities: Vec::new(),
modularity: 0.0,
community_count: 0,
};
}
// Initialize: each node in its own community
let mut community: Vec<u32> = (0..n as u32).collect();
// Total edge weight (m)
// For unweighted graph, m = edge_count / 2 (since each edge is counted twice if bidirectional)
// But Uni GraphProjection might be directed.
// Louvain usually works on undirected graphs.
// We treat it as undirected by summing all out_degrees.
let mut m: f64 = 0.0;
let mut node_weights = vec![0.0; n];
for v in 0..n as u32 {
let mut deg = graph.out_degree(v) as f64;
if graph.has_reverse() {
deg += graph.in_degree(v) as f64;
}
m += deg;
node_weights[v as usize] = deg;
}
m /= 2.0;
if m == 0.0 {
return LouvainResult {
communities: community
.into_iter()
.enumerate()
.map(|(i, c)| (graph.to_vid(i as u32), c as u64))
.collect(),
modularity: 0.0,
community_count: n,
};
}
// Track community total weights (Sigma_tot)
let mut community_weights = node_weights.clone();
for _ in 0..config.max_iterations {
let mut improved = false;
// Phase 1: Local moves
for v in 0..n as u32 {
let v_idx = v as usize;
let current_comm = community[v_idx];
let v_weight = node_weights[v_idx];
// Find neighbor communities and weights to them (k_i,in)
let mut neighbor_comm_weights: HashMap<u32, f64> = HashMap::new();
for &u in graph.out_neighbors(v) {
let u_comm = community[u as usize];
*neighbor_comm_weights.entry(u_comm).or_insert(0.0) += 1.0;
}
if graph.has_reverse() {
for &u in graph.in_neighbors(v) {
let u_comm = community[u as usize];
*neighbor_comm_weights.entry(u_comm).or_insert(0.0) += 1.0;
}
}
let mut best_comm = current_comm;
let mut max_gain = 0.0;
// Remove v from current community
community_weights[current_comm as usize] -= v_weight;
// Iterate candidate communities in a deterministic (community-id)
// order so HashMap iteration-seed differences cannot flip an
// otherwise-tied best-community choice. This keeps the detected
// partition reproducible across runs.
let mut candidates: Vec<(u32, f64)> = neighbor_comm_weights
.iter()
.map(|(&c, &w)| (c, w))
.collect();
candidates.sort_unstable_by_key(|&(c, _)| c);
for &(target_comm, k_i_in) in &candidates {
let target_comm_weight = community_weights[target_comm as usize];
// Modularity gain formula:
// delta_Q = [ (Sigma_tot + k_i,in) / 2m - ((Sigma_tot + k_i)/2m)^2 ] - [ Sigma_tot/2m - (Sigma_tot/2m)^2 - (k_i/2m)^2 ]
// Simplified: delta_Q = (1/2m) * (k_i,in - (Sigma_tot * k_i) / m)
let gain =
k_i_in - (target_comm_weight * v_weight * config.resolution) / (2.0 * m);
if gain > max_gain {
max_gain = gain;
best_comm = target_comm;
}
}
if max_gain > config.min_modularity_gain && best_comm != current_comm {
community[v_idx] = best_comm;
improved = true;
}
// Add v to best community
community_weights[community[v_idx] as usize] += v_weight;
}
if !improved {
break;
}
}
// Final modularity calculation
let q = compute_modularity(graph, &community, m, config.resolution);
// Map back to VIDs and renumber communities
let mut comm_map: HashMap<u32, u64> = HashMap::new();
let mut next_id = 0u64;
let mut results = Vec::with_capacity(n);
for (i, &comm) in community.iter().enumerate() {
let id = *comm_map.entry(comm).or_insert_with(|| {
let val = next_id;
next_id += 1;
val
});
results.push((graph.to_vid(i as u32), id));
}
LouvainResult {
communities: results,
modularity: q,
community_count: comm_map.len(),
}
}
}
fn compute_modularity(graph: &GraphProjection, community: &[u32], m: f64, resolution: f64) -> f64 {
let n = graph.vertex_count();
let mut q = 0.0;
// Sum over communities.
//
// `comm_total_weights` accumulates each community's *full undirected
// degree* `D_c`: every edge `v -> u` adds 1 to both endpoints' community
// totals. Summing out-degree alone (as before) under-counts the degree of
// every node that only appears as an edge target on a single-direction
// projection, mis-scaling `Q` relative to the undirected `m` and internal
// counts. `comm_internal_weights` counts each undirected internal edge
// once (`L_c`), matching the single-direction edge layout.
let mut comm_internal_weights: HashMap<u32, f64> = HashMap::new();
let mut comm_total_weights: HashMap<u32, f64> = HashMap::new();
for v in 0..n as u32 {
let v_comm = community[v as usize];
for &u in graph.out_neighbors(v) {
let u_comm = community[u as usize];
// Undirected degree: the edge contributes to both endpoints.
*comm_total_weights.entry(v_comm).or_insert(0.0) += 1.0;
*comm_total_weights.entry(u_comm).or_insert(0.0) += 1.0;
if u_comm == v_comm {
*comm_internal_weights.entry(v_comm).or_insert(0.0) += 1.0;
}
}
}
// The undirected modularity is `Q = Σ_c [ L_c / M − (D_c / 2M)^2 ]`, where
// `M = 2m` is the total number of undirected edges. Here `m` is the value
// `Louvain::run` derives (sum of out-degrees / 2), so `M = 2m` and the
// degree term denominator is `2M = 4m`.
let two_m = 2.0 * m;
for (&comm, &internal) in &comm_internal_weights {
let total = comm_total_weights[&comm];
q += (internal / two_m) - resolution * (total / (2.0 * two_m)).powi(2);
}
q
}
#[cfg(test)]
mod tests {
use super::*;
use crate::algo::test_utils::build_test_graph;
/// Regression: `compute_modularity` mis-scales directed degree vs internal.
///
/// `comm_total_weights` sums out-degree only while `comm_internal_weights`
/// counts each undirected internal edge once and `m = sum(out_degree) / 2`.
/// On a directed (single-direction) projection these conventions disagree,
/// so the reported modularity `Q` is wrong for the natural partition.
///
/// Two triangles {0,1,2} and {3,4,5} joined by the single bridge edge 2-3,
/// represented as 7 single-direction edges, give `m = 3.5`. The natural
/// 2-community partition has correct undirected modularity `Q = 0.3571`
/// (M = 7, internal = 3 per community, D_c = 7 per community).
// Rust guideline compliant
#[test]
fn test_louvain_modularity_scaling() {
// Two triangles plus a bridge, each undirected edge written once.
// Triangle A: 0-1, 1-2, 0-2 ; Triangle B: 3-4, 4-5, 3-5 ; bridge 2-3.
let vids = (0..6).map(Vid::from).collect::<Vec<_>>();
let edges = vec![
(Vid::from(0), Vid::from(1)),
(Vid::from(1), Vid::from(2)),
(Vid::from(0), Vid::from(2)),
(Vid::from(3), Vid::from(4)),
(Vid::from(4), Vid::from(5)),
(Vid::from(3), Vid::from(5)),
(Vid::from(2), Vid::from(3)),
];
let graph = build_test_graph(vids, edges);
// Natural 2-community partition: {0,1,2} -> 0, {3,4,5} -> 1.
let community: Vec<u32> = vec![0, 0, 0, 1, 1, 1];
// m as `Louvain::run` derives it for a no-reverse projection:
// sum of out-degrees / 2 = 7 / 2 = 3.5.
let m: f64 = (0..graph.vertex_count() as u32)
.map(|v| graph.out_degree(v) as f64)
.sum::<f64>()
/ 2.0;
let q = compute_modularity(&graph, &community, m, 1.0);
// Correct undirected modularity for this partition is 0.3571.
// RED today: the directed degree/internal mis-scaling yields ~0.3469.
assert!(
(q - 0.3571).abs() < 1e-3,
"modularity should be ~0.3571, got {q}"
);
}
}