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//! Leiden community detection algorithm
//!
//! Improves upon Louvain algorithm by adding a refinement phase that prevents
//! poorly connected communities. Implements hierarchical clustering for multi-level
//! community structure.
//!
//! Reference: "From Louvain to Leiden: guaranteeing well-connected communities"
//! Traag, Waltman & van Eck (2019)
use petgraph::graph::{Graph, NodeIndex};
use petgraph::Undirected;
use rand::rngs::StdRng;
use rand::SeedableRng;
use std::collections::{HashMap, HashSet};
use crate::Result;
/// (levels: map of `level → (node → community)`, hierarchy: `child_level → parent_level`).
type HierarchicalLeidenResult = (
HashMap<usize, HashMap<NodeIndex, usize>>,
HashMap<usize, Option<usize>>,
);
/// Metadata about an entity in the graph
#[derive(Debug, Clone, serde::Serialize, serde::Deserialize)]
pub struct EntityMetadata {
/// Unique entity identifier
pub id: String,
/// Entity name
pub name: String,
/// Entity type (e.g., "person", "organization")
pub entity_type: String,
/// Extraction confidence (0.0-1.0)
pub confidence: f32,
/// Number of mentions across documents
pub mention_count: usize,
}
/// Hierarchical community detection results
#[derive(Debug, Clone, serde::Serialize, serde::Deserialize)]
pub struct HierarchicalCommunities {
/// Communities at each hierarchical level
/// Level 0 = finest granularity, higher = coarser
pub levels: HashMap<usize, HashMap<NodeIndex, usize>>,
/// Parent-child relationships between levels
/// Maps community ID at level N to parent community ID at level N+1
pub hierarchy: HashMap<usize, Option<usize>>,
/// LLM-generated summaries for each community (optional)
pub summaries: HashMap<usize, String>,
/// Mapping from entity names to metadata (enriched from KnowledgeGraph)
pub entity_mapping: Option<HashMap<String, EntityMetadata>>,
}
impl HierarchicalCommunities {
/// Get all entities in a specific community at a given level
///
/// # Arguments
/// * `level` - Hierarchical level (0 = finest)
/// * `community_id` - Community identifier
/// * `graph` - The original graph to extract entity names from
///
/// # Returns
/// Vec of entity names in the community
pub fn get_community_entities(
&self,
level: usize,
community_id: usize,
graph: &Graph<String, f32, Undirected>,
) -> Vec<String> {
if let Some(level_communities) = self.levels.get(&level) {
level_communities
.iter()
.filter(|(_, &comm_id)| comm_id == community_id)
.filter_map(|(&node_idx, _)| graph.node_weight(node_idx))
.cloned()
.collect()
} else {
Vec::new()
}
}
/// Get entity metadata for entities in a community
///
/// # Arguments
/// * `entity_names` - List of entity names
///
/// # Returns
/// Vec of EntityMetadata for the entities
pub fn get_entities_metadata(&self, entity_names: &[String]) -> Vec<EntityMetadata> {
if let Some(mapping) = &self.entity_mapping {
entity_names
.iter()
.filter_map(|name| mapping.get(name).cloned())
.collect()
} else {
Vec::new()
}
}
/// Get community statistics
///
/// # Arguments
/// * `level` - Hierarchical level
/// * `community_id` - Community identifier
/// * `graph` - The original graph
///
/// # Returns
/// Tuple of (entity_count, avg_confidence, unique_types)
pub fn get_community_stats(
&self,
level: usize,
community_id: usize,
graph: &Graph<String, f32, Undirected>,
) -> (usize, f32, HashSet<String>) {
let entities = self.get_community_entities(level, community_id, graph);
let metadata = self.get_entities_metadata(&entities);
let count = metadata.len();
let avg_conf = if !metadata.is_empty() {
metadata.iter().map(|m| m.confidence).sum::<f32>() / count as f32
} else {
0.0
};
let types: HashSet<String> = metadata.iter().map(|m| m.entity_type.clone()).collect();
(count, avg_conf, types)
}
/// Generate extractive summary for a community (bottom-up approach)
///
/// Creates a summary by listing key entities and their types.
/// For use with LLM-based summarization, use `prepare_community_context()`.
///
/// # Arguments
/// * `level` - Hierarchical level
/// * `community_id` - Community identifier
/// * `graph` - The original graph
/// * `max_length` - Maximum summary length in characters
///
/// # Returns
/// Generated summary string
pub fn generate_community_summary(
&mut self,
level: usize,
community_id: usize,
graph: &Graph<String, f32, Undirected>,
max_length: usize,
) -> String {
let entities = self.get_community_entities(level, community_id, graph);
let metadata = self.get_entities_metadata(&entities);
if metadata.is_empty() {
return format!("Community {community_id} at level {level}: No entities");
}
// Group by entity type
let mut by_type: HashMap<String, Vec<&EntityMetadata>> = HashMap::new();
for meta in &metadata {
by_type
.entry(meta.entity_type.clone())
.or_default()
.push(meta);
}
// Build summary
let mut summary_parts = vec![
format!("Community {community_id} (Level {level})"),
format!("Contains {} entities:", metadata.len()),
];
for (entity_type, entities) in &by_type {
let names: Vec<String> = entities
.iter()
.take(5) // Limit to top 5 per type
.map(|e| e.name.clone())
.collect();
let more = if entities.len() > 5 {
format!(" and {} more", entities.len() - 5)
} else {
String::new()
};
summary_parts.push(format!("- {}: {}{}", entity_type, names.join(", "), more));
}
let summary = summary_parts.join("\n");
// Truncate if too long
if summary.len() > max_length {
format!("{}...", &summary[..max_length.saturating_sub(3)])
} else {
summary
}
}
/// Generate summaries for all communities at a specific level
///
/// # Arguments
/// * `level` - Hierarchical level to summarize
/// * `graph` - The original graph
/// * `max_length` - Maximum summary length per community
pub fn generate_level_summaries(
&mut self,
level: usize,
graph: &Graph<String, f32, Undirected>,
max_length: usize,
) {
if let Some(level_communities) = self.levels.get(&level) {
let community_ids: HashSet<usize> = level_communities.values().copied().collect();
for community_id in community_ids {
let summary =
self.generate_community_summary(level, community_id, graph, max_length);
self.summaries.insert(community_id, summary);
}
}
}
/// Generate summaries for all levels bottom-up
///
/// Starts from the finest level (0) and works up through the hierarchy.
/// Higher-level summaries can reference lower-level summaries.
///
/// # Arguments
/// * `graph` - The original graph
/// * `max_length` - Maximum summary length per community
pub fn generate_hierarchical_summaries(
&mut self,
graph: &Graph<String, f32, Undirected>,
max_length: usize,
) {
let max_level = self.levels.keys().max().copied().unwrap_or(0);
// Generate summaries bottom-up
for level in 0..=max_level {
self.generate_level_summaries(level, graph, max_length);
}
}
/// Prepare context for LLM-based community summarization
///
/// Generates a structured prompt containing:
/// - Entity names and types
/// - Relationships within the community
/// - Sub-community summaries (for higher levels)
///
/// # Arguments
/// * `level` - Hierarchical level
/// * `community_id` - Community identifier
/// * `graph` - The original graph
/// * `knowledge_graph` - The full KnowledgeGraph for relationship access
///
/// # Returns
/// Formatted context string ready for LLM input
#[cfg(feature = "async")]
pub fn prepare_community_context(
&self,
level: usize,
community_id: usize,
graph: &Graph<String, f32, Undirected>,
knowledge_graph: &crate::core::KnowledgeGraph,
) -> String {
let entities = self.get_community_entities(level, community_id, graph);
let metadata = self.get_entities_metadata(&entities);
let mut context_parts = vec![
format!("# Community {} at Level {}", community_id, level),
String::new(),
"## Entities:".to_string(),
];
// Add entity information
for meta in &metadata {
context_parts.push(format!(
"- {} ({}): confidence {:.2}, {} mentions",
meta.name, meta.entity_type, meta.confidence, meta.mention_count
));
}
context_parts.push(String::new());
context_parts.push("## Relationships:".to_string());
// Add relationships between entities in this community
let entity_set: HashSet<String> = entities.iter().cloned().collect();
for rel in knowledge_graph.get_all_relationships() {
// Check if both source and target are in this community
if let (Some(src_entity), Some(tgt_entity)) = (
knowledge_graph.get_entity(&rel.source),
knowledge_graph.get_entity(&rel.target),
) {
if entity_set.contains(&src_entity.name) && entity_set.contains(&tgt_entity.name) {
context_parts.push(format!(
"- {} --[{}]--> {} (confidence: {:.2})",
src_entity.name, rel.relation_type, tgt_entity.name, rel.confidence
));
}
}
}
// For higher levels, include sub-community summaries
if level > 0 {
context_parts.push(String::new());
context_parts.push("## Sub-community Summaries:".to_string());
// Would need to track parent-child relationships to list sub-communities
}
context_parts.join("\n")
}
/// Retrieve relevant communities using adaptive query routing
///
/// Automatically selects the appropriate hierarchical level based on query complexity
/// and returns matching community summaries.
///
/// # Arguments
/// * `query` - User query string
/// * `graph` - The original graph
/// * `router_config` - Configuration for adaptive routing
///
/// # Returns
/// Vec of (level, community_id, summary) tuples
///
/// # Example
/// ```no_run
/// use graphrag_core::query::AdaptiveRoutingConfig;
///
/// let config = AdaptiveRoutingConfig::default();
/// let results = communities.adaptive_retrieve("AI overview", &graph, config);
/// ```
pub fn adaptive_retrieve(
&self,
query: &str,
graph: &Graph<String, f32, Undirected>,
router_config: crate::query::AdaptiveRoutingConfig,
) -> Vec<(usize, usize, String)> {
use crate::query::QueryComplexityAnalyzer;
// Analyze query and determine level
let analyzer = QueryComplexityAnalyzer::new(router_config);
let suggested_level = analyzer.suggest_level(query);
// Retrieve at suggested level
self.retrieve_at_level(query, graph, suggested_level)
}
/// Retrieve relevant communities at a specific hierarchical level
///
/// # Arguments
/// * `query` - User query string
/// * `graph` - The original graph
/// * `level` - Hierarchical level to search (0 = finest)
///
/// # Returns
/// Vec of (level, community_id, summary) tuples
pub fn retrieve_at_level(
&self,
query: &str,
graph: &Graph<String, f32, Undirected>,
level: usize,
) -> Vec<(usize, usize, String)> {
let mut results = Vec::new();
let query_lower = query.to_lowercase();
// Get all communities at this level
if let Some(level_communities) = self.levels.get(&level) {
let unique_communities: HashSet<usize> = level_communities.values().copied().collect();
for community_id in unique_communities {
let entities = self.get_community_entities(level, community_id, graph);
// Check relevance
let is_relevant = entities
.iter()
.any(|entity| entity.to_lowercase().contains(&query_lower));
if is_relevant {
// Get or generate summary
let summary = self
.summaries
.get(&community_id)
.cloned()
.unwrap_or_else(|| {
// Fallback: create entity list
format!("Entities: {}", entities.join(", "))
});
results.push((level, community_id, summary));
}
}
}
results
}
/// Retrieve with detailed query analysis
///
/// Returns both the retrieval results and the query analysis that determined the level.
///
/// # Arguments
/// * `query` - User query string
/// * `graph` - The original graph
/// * `router_config` - Configuration for adaptive routing
///
/// # Returns
/// Tuple of (QueryAnalysis, retrieval results)
pub fn adaptive_retrieve_detailed(
&self,
query: &str,
graph: &Graph<String, f32, Undirected>,
router_config: crate::query::AdaptiveRoutingConfig,
) -> (crate::query::QueryAnalysis, Vec<(usize, usize, String)>) {
use crate::query::QueryComplexityAnalyzer;
// Analyze query
let analyzer = QueryComplexityAnalyzer::new(router_config);
let analysis = analyzer.analyze_detailed(query);
// Retrieve at suggested level
let results = self.retrieve_at_level(query, graph, analysis.suggested_level);
(analysis, results)
}
}
/// Configuration for Leiden algorithm
#[derive(Debug, Clone, serde::Serialize, serde::Deserialize)]
pub struct LeidenConfig {
/// Maximum community size
pub max_cluster_size: usize,
/// Use only largest connected component
pub use_lcc: bool,
/// Random seed for reproducibility
pub seed: Option<u64>,
/// Modularity resolution parameter (default: 1.0)
/// Lower = larger communities, Higher = smaller communities
pub resolution: f32,
/// Maximum hierarchical depth
pub max_levels: usize,
/// Minimum improvement to continue iterations
pub min_improvement: f32,
}
impl Default for LeidenConfig {
fn default() -> Self {
Self {
max_cluster_size: 10,
use_lcc: true,
seed: None,
resolution: 1.0,
max_levels: 5,
min_improvement: 0.001,
}
}
}
/// Leiden community detection algorithm
pub struct LeidenCommunityDetector {
config: LeidenConfig,
}
impl LeidenCommunityDetector {
/// Create a new Leiden detector with configuration
pub fn new(config: LeidenConfig) -> Self {
Self { config }
}
/// Detect hierarchical communities in graph
pub fn detect_communities(
&self,
graph: &Graph<String, f32, Undirected>,
) -> Result<HierarchicalCommunities> {
// 1. Optionally extract largest connected component
let working_graph = if self.config.use_lcc {
self.extract_largest_connected_component(graph)
} else {
graph.clone()
};
// 2. Initialize RNG with seed if provided
let mut _rng = match self.config.seed {
Some(seed) => StdRng::seed_from_u64(seed),
None => StdRng::from_entropy(),
};
// 3. Run hierarchical Leiden clustering
let (levels, hierarchy) = self.hierarchical_leiden(&working_graph)?;
Ok(HierarchicalCommunities {
levels,
hierarchy,
summaries: HashMap::new(), // Filled later by LLM if needed
entity_mapping: None, // Enriched when called from KnowledgeGraph
})
}
/// Hierarchical Leiden algorithm implementation
fn hierarchical_leiden(
&self,
graph: &Graph<String, f32, Undirected>,
) -> Result<HierarchicalLeidenResult> {
let mut levels = HashMap::new();
let hierarchy = HashMap::new();
let current_graph = graph.clone();
let level = 0;
// Phase 1: Initialize each node in its own community
let mut communities = self.initialize_communities(¤t_graph);
// Phase 2: Local moving (greedy modularity optimization)
let mut improved = true;
let mut iteration = 0;
const MAX_ITERATIONS: usize = 100;
while improved && iteration < MAX_ITERATIONS {
improved = false;
for node in current_graph.node_indices() {
let best_community = self.find_best_community(¤t_graph, node, &communities);
if best_community != communities[&node] {
communities.insert(node, best_community);
improved = true;
}
}
iteration += 1;
}
// Phase 3: Refinement (KEY difference from Louvain)
communities = self.refine_partition(¤t_graph, communities)?;
// Store this level
levels.insert(level, communities);
Ok((levels, hierarchy))
}
/// Initialize each node in its own community
fn initialize_communities(
&self,
graph: &Graph<String, f32, Undirected>,
) -> HashMap<NodeIndex, usize> {
graph
.node_indices()
.enumerate()
.map(|(i, node)| (node, i))
.collect()
}
/// Find best community for a node using greedy modularity optimization
fn find_best_community(
&self,
graph: &Graph<String, f32, Undirected>,
node: NodeIndex,
communities: &HashMap<NodeIndex, usize>,
) -> usize {
let current_community = communities[&node];
let mut best_community = current_community;
let mut best_delta_modularity = 0.0;
// Get neighboring communities
let neighbor_communities: HashSet<usize> = graph
.neighbors(node)
.filter_map(|neighbor| communities.get(&neighbor).copied())
.collect();
// Try each neighboring community
for &neighbor_community in &neighbor_communities {
if neighbor_community == current_community {
continue;
}
let delta = self.calculate_modularity_delta(
graph,
node,
current_community,
neighbor_community,
communities,
);
if delta > best_delta_modularity {
best_delta_modularity = delta;
best_community = neighbor_community;
}
}
best_community
}
/// Refine partition to ensure well-connected communities
/// KEY difference from Louvain - prevents poorly connected communities
fn refine_partition(
&self,
graph: &Graph<String, f32, Undirected>,
mut communities: HashMap<NodeIndex, usize>,
) -> Result<HashMap<NodeIndex, usize>> {
// Get unique community IDs
let community_ids: HashSet<usize> = communities.values().copied().collect();
for &community_id in &community_ids {
// Get nodes in this community
let community_nodes: Vec<NodeIndex> = communities
.iter()
.filter(|(_, &c)| c == community_id)
.map(|(&n, _)| n)
.collect();
// Check if community is well-connected
if !self.is_well_connected(graph, &community_nodes) {
// Split poorly connected community
self.split_community(graph, &mut communities, &community_nodes)?;
}
}
Ok(communities)
}
/// Check if community forms a connected subgraph
fn is_well_connected(
&self,
graph: &Graph<String, f32, Undirected>,
nodes: &[NodeIndex],
) -> bool {
if nodes.len() <= 1 {
return true;
}
// DFS to check connectivity
let mut visited = HashSet::new();
let mut stack = vec![nodes[0]];
visited.insert(nodes[0]);
while let Some(node) = stack.pop() {
for neighbor in graph.neighbors(node) {
if nodes.contains(&neighbor) && !visited.contains(&neighbor) {
visited.insert(neighbor);
stack.push(neighbor);
}
}
}
visited.len() == nodes.len()
}
/// Split poorly connected community into well-connected sub-communities
fn split_community(
&self,
graph: &Graph<String, f32, Undirected>,
communities: &mut HashMap<NodeIndex, usize>,
nodes: &[NodeIndex],
) -> Result<()> {
// Find connected components within community
let components = self.find_connected_components(graph, nodes);
// Assign new community IDs to each component
let max_community_id = communities.values().max().copied().unwrap_or(0);
for (idx, component) in components.iter().enumerate() {
let new_community_id = max_community_id + idx + 1;
for &node in component {
communities.insert(node, new_community_id);
}
}
Ok(())
}
/// Find connected components within a set of nodes
fn find_connected_components(
&self,
graph: &Graph<String, f32, Undirected>,
nodes: &[NodeIndex],
) -> Vec<Vec<NodeIndex>> {
let mut components = Vec::new();
let mut unvisited: HashSet<NodeIndex> = nodes.iter().copied().collect();
while !unvisited.is_empty() {
let start = *unvisited.iter().next().expect("non-empty checked above");
let mut component = Vec::new();
let mut stack = vec![start];
while let Some(node) = stack.pop() {
if !unvisited.remove(&node) {
continue;
}
component.push(node);
for neighbor in graph.neighbors(node) {
if unvisited.contains(&neighbor) && nodes.contains(&neighbor) {
stack.push(neighbor);
}
}
}
components.push(component);
}
components
}
/// Calculate modularity delta for moving node between communities
fn calculate_modularity_delta(
&self,
graph: &Graph<String, f32, Undirected>,
node: NodeIndex,
from_community: usize,
to_community: usize,
communities: &HashMap<NodeIndex, usize>,
) -> f32 {
let degree = graph.edges(node).count() as f32;
let total_edges = graph.edge_count() as f32 * 2.0; // Undirected
// Edges to communities
let k_i_in_to = self.edges_to_community(graph, node, to_community, communities);
let k_i_in_from = self.edges_to_community(graph, node, from_community, communities);
// Total degree of communities
let sigma_tot_to = self.total_degree_of_community(graph, to_community, communities);
let sigma_tot_from = self.total_degree_of_community(graph, from_community, communities);
// Delta Q using Newman's modularity formula
((k_i_in_to as f32 - k_i_in_from as f32) / total_edges)
- self.config.resolution
* degree
* ((sigma_tot_to - sigma_tot_from + degree) / (total_edges * total_edges))
}
/// Count edges from node to a specific community
fn edges_to_community(
&self,
graph: &Graph<String, f32, Undirected>,
node: NodeIndex,
community: usize,
communities: &HashMap<NodeIndex, usize>,
) -> usize {
graph
.neighbors(node)
.filter(|&neighbor| communities.get(&neighbor) == Some(&community))
.count()
}
/// Calculate total degree of all nodes in a community
fn total_degree_of_community(
&self,
graph: &Graph<String, f32, Undirected>,
community: usize,
communities: &HashMap<NodeIndex, usize>,
) -> f32 {
communities
.iter()
.filter(|(_, &c)| c == community)
.map(|(&node, _)| graph.edges(node).count() as f32)
.sum()
}
/// Extract largest connected component from graph
fn extract_largest_connected_component(
&self,
graph: &Graph<String, f32, Undirected>,
) -> Graph<String, f32, Undirected> {
use petgraph::algo::connected_components;
let num_components = connected_components(graph);
if num_components == 1 {
return graph.clone();
}
// For now, return original graph
// Full implementation would extract actual largest component
graph.clone()
}
}
#[cfg(test)]
mod tests {
use super::*;
fn create_test_graph() -> Graph<String, f32, Undirected> {
let mut graph = Graph::new_undirected();
// Create simple graph with 2 obvious communities
let n0 = graph.add_node("A".to_string());
let n1 = graph.add_node("B".to_string());
let n2 = graph.add_node("C".to_string());
let n3 = graph.add_node("D".to_string());
// Community 1: A-B-C (triangle)
graph.add_edge(n0, n1, 1.0);
graph.add_edge(n1, n2, 1.0);
graph.add_edge(n2, n0, 1.0);
// Community 2: D (isolated)
// One weak link between communities
graph.add_edge(n2, n3, 0.1);
graph
}
#[test]
fn test_leiden_basic() {
let graph = create_test_graph();
let config = LeidenConfig::default();
let detector = LeidenCommunityDetector::new(config);
let result = detector.detect_communities(&graph);
assert!(result.is_ok());
let communities = result.unwrap();
assert!(!communities.levels.is_empty());
}
#[test]
fn test_is_well_connected() {
let graph = create_test_graph();
let config = LeidenConfig::default();
let detector = LeidenCommunityDetector::new(config);
// First 3 nodes form connected triangle
let nodes = vec![NodeIndex::new(0), NodeIndex::new(1), NodeIndex::new(2)];
assert!(detector.is_well_connected(&graph, &nodes));
}
#[test]
fn test_config_defaults() {
let config = LeidenConfig::default();
assert_eq!(config.max_cluster_size, 10);
assert_eq!(config.resolution, 1.0);
assert_eq!(config.max_levels, 5);
assert!(config.use_lcc);
}
}