Community Detection

<h2 id="community-detection-in-geode" class="position-relative d-flex align-items-center group"> Community Detection in Geode <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="community-detection-in-geode" aria-haspopup="dialog" aria-label="Share link: Community Detection in Geode"> Share link </button> </h2><div id="headingShareModal" class="heading-share-modal" role="dialog" aria-modal="true" aria-labelledby="headingShareTitle" hidden> <div class="hsm-dialog" role="document"> <div class="hsm-header"> <h2 id="headingShareTitle" class="h6 mb-0 fw-bold">Share this section</h2> <button type="button" class="hsm-close" aria-label="Close"> </button> </div> <div class="hsm-body"> <label for="headingShareInput" class="form-label small text-muted mb-1 text-uppercase fw-bold" style="font-size: 0.7rem; letter-spacing: 0.5px;">Permalink</label> <div class="input-group mb-4 hsm-url-group"> <input id="headingShareInput" type="text" class="form-control font-monospace" readonly aria-readonly="true" style="font-size: 0.85rem;" /> <button class="btn btn-primary hsm-copy" type="button" aria-label="Copy" title="Copy"> </button> </div> <div class="small fw-bold mb-2 text-muted text-uppercase" style="font-size: 0.7rem; 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Geode provides native GQL support for implementing various community detection algorithms efficiently at scale. <h3 id="understanding-community-detection" class="position-relative d-flex align-items-center group"> Understanding Community Detection <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="understanding-community-detection" aria-haspopup="dialog" aria-label="Share link: Understanding Community Detection"> Share link </button> </h3>Communities are subgraphs where nodes have more connections within the group than to nodes outside it. Detecting these structures helps understand graph organization, identify influential groups, and optimize resource allocation. <h4 id="core-concepts" class="position-relative d-flex align-items-center group"> Core Concepts <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="core-concepts" aria-haspopup="dialog" aria-label="Share link: Core Concepts"> Share link </button> </h4>Modularity: A metric measuring the quality of a community partition, comparing actual intra-community edges to expected edges in a random graph. Label Propagation: An iterative algorithm where nodes adopt the most common label among their neighbors, causing communities to emerge naturally. Connected Components: The simplest form of community detection, identifying completely disconnected subgraphs. Overlapping Communities: Some algorithms allow nodes to belong to multiple communities simultaneously, reflecting real-world complexity. <h3 id="label-propagation-algorithm" class="position-relative d-flex align-items-center group"> Label Propagation Algorithm <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="label-propagation-algorithm" aria-haspopup="dialog" aria-label="Share link: Label Propagation Algorithm"> Share link </button> </h3>Label propagation is a fast, simple community detection method that works well for large graphs. <h4 id="basic-implementation" class="position-relative d-flex align-items-center group"> Basic Implementation <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="basic-implementation" aria-haspopup="dialog" aria-label="Share link: Basic Implementation"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Initialize each node with unique label MATCH (n:User) SET n.community = ID(n); -- Iterative label propagation MATCH (n:User)-[:KNOWS]-(neighbor:User) WITH n, neighbor.community AS label, COUNT(*) AS frequency ORDER BY frequency DESC WITH n, COLLECT(label)[0] AS most_common_label SET n.community_new = most_common_label; -- Update labels MATCH (n:User) SET n.community = n.community_new REMOVE n.community_new; -- Find community sizes MATCH (n:User) RETURN n.community AS community_id, COUNT(n) AS size, COLLECT(n.id)[..10] AS sample_members ORDER BY size DESC; </code></pre></div> <h4 id="weighted-label-propagation" class="position-relative d-flex align-items-center group"> Weighted Label Propagation <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="weighted-label-propagation" aria-haspopup="dialog" aria-label="Share link: Weighted Label Propagation"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Propagate labels weighted by edge strength MATCH (n:User)-[r:INTERACTS_WITH]-(neighbor:User) WITH n, neighbor.community AS label, SUM(r.weight) AS total_weight ORDER BY total_weight DESC WITH n, COLLECT(label)[0] AS strongest_label SET n.community = strongest_label; </code></pre></div> <h4 id="synchronized-vs-asynchronous-updates" class="position-relative d-flex align-items-center group"> Synchronized vs Asynchronous Updates <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="synchronized-vs-asynchronous-updates" aria-haspopup="dialog" aria-label="Share link: Synchronized vs Asynchronous Updates"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Synchronized update (process all nodes simultaneously) MATCH (n:User)-[:KNOWS]-(neighbor:User) WITH n, neighbor.community AS label, COUNT(*) AS freq ORDER BY freq DESC WITH n, COLLECT(label)[0] AS new_label CALL { WITH n, new_label SET n.community_new = new_label } IN TRANSACTIONS OF 10000 ROWS; MATCH (n:User) SET n.community = n.community_new REMOVE n.community_new; </code></pre></div> <h3 id="connected-components" class="position-relative d-flex align-items-center group"> Connected Components <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="connected-components" aria-haspopup="dialog" aria-label="Share link: Connected Components"> Share link </button> </h3>Connected components identify completely separate subgraphs with no paths between them. <h4 id="finding-connected-components" class="position-relative d-flex align-items-center group"> Finding Connected Components <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="finding-connected-components" aria-haspopup="dialog" aria-label="Share link: Finding Connected Components"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Initialize component IDs MATCH (n:Node) SET n.component = ID(n); -- Propagate minimum ID within each component MATCH (n:Node)-[:CONNECTED]-(neighbor:Node) WHERE neighbor.component < n.component SET n.component = neighbor.component; -- Repeat until stable (typically log(N) iterations) -- Then analyze components MATCH (n:Node) RETURN n.component AS component_id, COUNT(n) AS size, COLLECT(n.name) AS members ORDER BY size DESC; </code></pre></div> <h4 id="strongly-connected-components" class="position-relative d-flex align-items-center group"> Strongly Connected Components <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="strongly-connected-components" aria-haspopup="dialog" aria-label="Share link: Strongly Connected Components"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- For directed graphs, find strongly connected components MATCH path = (start:Node)-[:DIRECTED_EDGE*]->(end:Node) WHERE start = end AND LENGTH(path) > 0 WITH DISTINCT [node IN NODES(path) | ID(node)] AS component_nodes RETURN component_nodes, SIZE(component_nodes) AS component_size ORDER BY component_size DESC; </code></pre></div> <h3 id="modularity-based-detection" class="position-relative d-flex align-items-center group"> Modularity-Based Detection <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="modularity-based-detection" aria-haspopup="dialog" aria-label="Share link: Modularity-Based Detection"> Share link </button> </h3>Modularity optimization finds communities that maximize the modularity metric. <h4 id="computing-modularity" class="position-relative d-flex align-items-center group"> Computing Modularity <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="computing-modularity" aria-haspopup="dialog" aria-label="Share link: Computing Modularity"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Calculate modularity for current community assignment MATCH (n:Node) WITH COUNT(n) AS total_nodes MATCH (n:Node)-[r:CONNECTED]-(m:Node) WITH total_nodes, COUNT(r) / 2.0 AS total_edges, COLLECT({ node: n, degree: COUNT { (n)-[:CONNECTED]-() }, community: n.community }) AS node_data WITH total_nodes, total_edges, node_data MATCH (n:Node)-[:CONNECTED]-(m:Node) WHERE n.community = m.community WITH total_edges, node_data, COUNT(*) / 2.0 AS intra_community_edges, SUM([nd IN node_data WHERE nd.community = n.community | nd.degree][0]) AS community_degree_sum RETURN (intra_community_edges / total_edges) - POWER(community_degree_sum / (2.0 * total_edges), 2) AS modularity; </code></pre></div> <h4 id="greedy-modularity-optimization" class="position-relative d-flex align-items-center group"> Greedy Modularity Optimization <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="greedy-modularity-optimization" aria-haspopup="dialog" aria-label="Share link: Greedy Modularity Optimization"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Iteratively move nodes to communities that maximize modularity gain MATCH (n:Node) SET n.community = ID(n); -- For each node, try moving to neighbor communities MATCH (n:Node)-[:CONNECTED]-(neighbor:Node) WHERE n.community <> neighbor.community WITH n, neighbor.community AS candidate_community, COUNT(*) AS edge_count ORDER BY edge_count DESC WITH n, COLLECT(candidate_community)[0] AS best_community WHERE best_community IS NOT NULL SET n.community = best_community; -- Repeat until modularity stops improving </code></pre></div> <h3 id="louvain-algorithm" class="position-relative d-flex align-items-center group"> Louvain Algorithm <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="louvain-algorithm" aria-haspopup="dialog" aria-label="Share link: Louvain Algorithm"> Share link </button> </h3>The Louvain method is a hierarchical community detection algorithm that optimizes modularity. <h4 id="phase-1-local-optimization" class="position-relative d-flex align-items-center group"> Phase 1: Local Optimization <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="phase-1-local-optimization" aria-haspopup="dialog" aria-label="Share link: Phase 1: Local Optimization"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Initialize communities MATCH (n:Node) SET n.community = ID(n); -- Local optimization: move nodes to maximize modularity gain MATCH (n:Node) CALL { WITH n MATCH (n)-[r:CONNECTED]-(neighbor:Node) WITH neighbor.community AS comm, SUM(r.weight) AS edge_weight, COUNT { (neighbor)-[:CONNECTED]-(:Node {community: neighbor.community}) } AS comm_edges RETURN comm, edge_weight - (comm_edges * COUNT { (n)-[:CONNECTED]-() } / (2.0 * COUNT { MATCH ()-[:CONNECTED]-() })) AS modularity_gain ORDER BY modularity_gain DESC LIMIT 1 } SET n.community = comm; </code></pre></div> <h4 id="phase-2-graph-aggregation" class="position-relative d-flex align-items-center group"> Phase 2: Graph Aggregation <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="phase-2-graph-aggregation" aria-haspopup="dialog" aria-label="Share link: Phase 2: Graph Aggregation"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Create super-nodes from communities MATCH (n:Node) WITH n.community AS comm_id, COLLECT(n) AS members, SUM(COUNT { (n)-[:CONNECTED]-() }) AS total_degree CREATE (super:SuperNode { id: comm_id, member_count: SIZE(members), total_degree: total_degree }); -- Create edges between super-nodes MATCH (n:Node)-[r:CONNECTED]-(m:Node) WHERE n.community <> m.community WITH n.community AS comm1, m.community AS comm2, SUM(r.weight) AS total_weight MATCH (s1:SuperNode {id: comm1}), (s2:SuperNode {id: comm2}) CREATE (s1)-[:CONNECTED {weight: total_weight}]->(s2); </code></pre></div> <h3 id="practical-applications" class="position-relative d-flex align-items-center group"> Practical Applications <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="practical-applications" aria-haspopup="dialog" aria-label="Share link: Practical Applications"> Share link </button> </h3> <h4 id="social-network-clustering" class="position-relative d-flex align-items-center group"> Social Network Clustering <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="social-network-clustering" aria-haspopup="dialog" aria-label="Share link: Social Network Clustering"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Detect friend groups in social network MATCH (user:User) SET user.friend_group = ID(user); -- Propagate group labels MATCH (u:User)-[:FRIENDS_WITH]-(friend:User) WITH u, friend.friend_group AS group, COUNT(*) AS mutual_friends ORDER BY mutual_friends DESC WITH u, COLLECT(group)[0] AS primary_group SET u.friend_group = primary_group; -- Analyze groups MATCH (u:User) WITH u.friend_group AS group_id, COUNT(u) AS size, AVG(COUNT { (u)-[:FRIENDS_WITH]-() }) AS avg_connections RETURN group_id, size, avg_connections ORDER BY size DESC; </code></pre></div> <h4 id="product-categorization" class="position-relative d-flex align-items-center group"> Product Categorization <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="product-categorization" aria-haspopup="dialog" aria-label="Share link: Product Categorization"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Discover product categories from purchase patterns MATCH (p:Product) SET p.category_cluster = ID(p); -- Products purchased together form categories MATCH (p1:Product)<-[:PURCHASED]-(c:Customer)-[:PURCHASED]->(p2:Product) WHERE ID(p1) < ID(p2) WITH p1, p2, COUNT(c) AS co_purchases WHERE co_purchases > 5 MERGE (p1)-[:RELATED {strength: co_purchases}]-(p2); -- Apply label propagation MATCH (p:Product)-[r:RELATED]-(other:Product) WITH p, other.category_cluster AS cluster, SUM(r.strength) AS total_strength ORDER BY total_strength DESC WITH p, COLLECT(cluster)[0] AS strongest_cluster SET p.category_cluster = strongest_cluster; </code></pre></div> <h4 id="knowledge-graph-clustering" class="position-relative d-flex align-items-center group"> Knowledge Graph Clustering <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="knowledge-graph-clustering" aria-haspopup="dialog" aria-label="Share link: Knowledge Graph Clustering"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Cluster entities by semantic relationships MATCH (e:Entity) SET e.topic_cluster = ID(e); MATCH (e1:Entity)-[:RELATED_TO]-(e2:Entity) WITH e1, e2.topic_cluster AS cluster, COUNT(*) AS relations ORDER BY relations DESC WITH e1, COLLECT(cluster)[0] AS primary_cluster SET e1.topic_cluster = primary_cluster; -- Identify cluster topics MATCH (e:Entity) WHERE e.topic_cluster IS NOT NULL WITH e.topic_cluster AS cluster_id, COLLECT(e.type) AS entity_types RETURN cluster_id, SIZE(entity_types) AS cluster_size, [type IN entity_types | type][..5] AS sample_types; </code></pre></div> <h3 id="performance-optimization" class="position-relative d-flex align-items-center group"> Performance Optimization <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="performance-optimization" aria-haspopup="dialog" aria-label="Share link: Performance Optimization"> Share link </button> </h3> <h4 id="batch-processing" class="position-relative d-flex align-items-center group"> Batch Processing <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="batch-processing" aria-haspopup="dialog" aria-label="Share link: Batch Processing"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Process large graphs in batches MATCH (n:Node) WHERE ID(n) % 100 < 10 -- Process 10% at a time WITH n CALL { WITH n MATCH (n)-[:CONNECTED]-(neighbor:Node) WITH n, neighbor.community AS label, COUNT(*) AS freq ORDER BY freq DESC LIMIT 1 SET n.community_temp = label } IN TRANSACTIONS OF 10000 ROWS; </code></pre></div> <h4 id="convergence-detection" class="position-relative d-flex align-items-center group"> Convergence Detection <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="convergence-detection" aria-haspopup="dialog" aria-label="Share link: Convergence Detection"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Check if communities have stabilized MATCH (n:Node) WITH SUM(CASE WHEN n.community = n.community_old THEN 0 ELSE 1 END) AS changes, COUNT(n) AS total RETURN changes, total, (changes * 100.0 / total) AS change_percentage, CASE WHEN changes * 100.0 / total < 1.0 THEN 'CONVERGED' ELSE 'CONTINUE' END AS status; </code></pre></div> <h4 id="parallel-community-assignment" class="position-relative d-flex align-items-center group"> Parallel Community Assignment <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="parallel-community-assignment" aria-haspopup="dialog" aria-label="Share link: Parallel Community Assignment"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Assign communities in parallel for independent subgraphs MATCH (n:Node) WHERE n.partition = 'A' -- Process partition A WITH n CALL { WITH n -- Community detection logic for partition A } IN TRANSACTIONS; MATCH (n:Node) WHERE n.partition = 'B' -- Process partition B in parallel WITH n CALL { WITH n -- Community detection logic for partition B } IN TRANSACTIONS; </code></pre></div> <h3 id="best-practices" class="position-relative d-flex align-items-center group"> Best Practices <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="best-practices" aria-haspopup="dialog" aria-label="Share link: Best Practices"> Share link </button> </h3> <h4 id="algorithm-selection" class="position-relative d-flex align-items-center group"> Algorithm Selection <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="algorithm-selection" aria-haspopup="dialog" aria-label="Share link: Algorithm Selection"> Share link </button> </h4>Label Propagation: Use for large graphs (millions of nodes) when speed is critical and approximate results are acceptable. Connected Components: Apply when looking for completely disconnected subgraphs or network islands. Modularity Optimization: Choose for high-quality communities when computation time is less critical. Louvain Method: Best for hierarchical community structure and balanced speed/quality tradeoff. <h4 id="parameter-tuning" class="position-relative d-flex align-items-center group"> Parameter Tuning <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="parameter-tuning" aria-haspopup="dialog" aria-label="Share link: Parameter Tuning"> Share link </button> </h4>Iteration Limit: Set maximum iterations (typically 10-50) to prevent infinite loops in label propagation. Weight Thresholds: Filter weak edges before community detection to improve result quality and performance. Resolution Parameter: Adjust modularity resolution to control community granularity (higher values create smaller communities). <h4 id="quality-validation" class="position-relative d-flex align-items-center group"> Quality Validation <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="quality-validation" aria-haspopup="dialog" aria-label="Share link: Quality Validation"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Measure community quality metrics MATCH (n:Node) WITH n.community AS comm, COUNT(n) AS size, SUM(COUNT { (n)-[:CONNECTED]-(:Node {community: comm}) }) AS internal_edges, SUM(COUNT { (n)-[:CONNECTED]-(:Node) WHERE NOT :Node {community: comm} }) AS external_edges RETURN comm, size, internal_edges, external_edges, internal_edges * 1.0 / (internal_edges + external_edges) AS density_ratio ORDER BY density_ratio DESC; </code></pre></div> <h3 id="integration-examples" class="position-relative d-flex align-items-center group"> Integration Examples <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="integration-examples" aria-haspopup="dialog" aria-label="Share link: Integration Examples"> Share link </button> </h3> <h4 id="python-client" class="position-relative d-flex align-items-center group"> Python Client <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="python-client" aria-haspopup="dialog" aria-label="Share link: Python Client"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python">from geode_client import Client async def detect_communities(client, max_iterations=20): # Initialize labels await client.execute(""" MATCH (n:User) SET n.community = ID(n) """) # Iterative label propagation for iteration in range(max_iterations): result, _ = await client.query(""" MATCH (n:User)-[:KNOWS]-(neighbor:User) WITH n, neighbor.community AS label, COUNT(*) AS freq ORDER BY freq DESC WITH n, COLLECT(label)[0] AS new_label SET n.community_new = new_label WITH SUM(CASE WHEN n.community = n.community_new THEN 0 ELSE 1 END) AS changes RETURN changes """) await client.execute("MATCH (n:User) SET n.community = n.community_new REMOVE n.community_new") changes = result.rows[0][0] if changes == 0: print(f"Converged after {iteration + 1} iterations") break # Get community statistics communities, _ = await client.query(""" MATCH (n:User) RETURN n.community AS id, COUNT(n) AS size, COLLECT(n.username)[..10] AS sample_members ORDER BY size DESC """) return communities.rows </code></pre></div> <h4 id="rust-client" class="position-relative d-flex align-items-center group"> Rust Client <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="rust-client" aria-haspopup="dialog" aria-label="Share link: Rust Client"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-rust" data-lang="rust">use geode_client::Client; async fn label_propagation(client: &Client, iterations: usize) -> Result<Vec<Community>> { // Initialize client.execute("MATCH (n:User) SET n.community = ID(n)").await?; // Propagate labels for i in 0..iterations { let changes = client.execute( "MATCH (n:User)-[:KNOWS]-(neighbor:User) \ WITH n, neighbor.community AS label, COUNT(*) AS freq \ ORDER BY freq DESC \ WITH n, COLLECT(label)[0] AS new_label \ SET n.community_new = new_label \ WITH SUM(CASE WHEN n.community = n.community_new THEN 0 ELSE 1 END) AS changes \ RETURN changes" ).await?; client.execute("MATCH (n:User) SET n.community = n.community_new REMOVE n.community_new").await?; if changes.get_int(0, 0)? == 0 { println!("Converged at iteration {}", i); break; } } // Extract communities let results = client.execute( "MATCH (n:User) \ RETURN n.community, COUNT(n) AS size \ ORDER BY size DESC" ).await?; Ok(results.into_communities()) } </code></pre></div> <h3 id="multi-level-community-detection" class="position-relative d-flex align-items-center group"> Multi-Level Community Detection <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="multi-level-community-detection" aria-haspopup="dialog" aria-label="Share link: Multi-Level Community Detection"> Share link </button> </h3> <h4 id="hierarchical-leiden-algorithm" class="position-relative d-flex align-items-center group"> Hierarchical Leiden Algorithm <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="hierarchical-leiden-algorithm" aria-haspopup="dialog" aria-label="Share link: Hierarchical Leiden Algorithm"> Share link </button> </h4>Improved version of Louvain with guaranteed well-connected communities: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Phase 1: Local moving with refinement MATCH (n:Node) SET n.community = ID(n); // Move nodes to improve modularity MATCH (n:Node)-[:CONNECTED]-(neighbor:Node) WITH n, neighbor.community AS comm, COUNT(*) AS edge_count ORDER BY edge_count DESC WITH n, COLLECT(comm)[0] AS best_community SET n.community = best_community; -- Phase 2: Refinement (merge poorly connected nodes) MATCH (n:Node) WHERE n.community IS NOT NULL CALL { WITH n MATCH (n)-[:CONNECTED]-(internal:Node {community: n.community}) WITH n, COUNT(internal) AS internal_degree MATCH (n)-[:CONNECTED]-(external:Node) WHERE external.community <> n.community WITH n, internal_degree, COUNT(external) AS external_degree WHERE internal_degree < external_degree SET n.needs_refinement = true } IN TRANSACTIONS; -- Phase 3: Aggregate graph MATCH (n:Node) WITH n.community AS comm_id, COLLECT(n) AS members, SUM(SIZE((n)-[:CONNECTED]-())) AS total_degree CREATE (super:SuperNode { id: comm_id, size: SIZE(members), total_degree: total_degree }); MATCH (n1:Node)-[r:CONNECTED]-(n2:Node) WHERE n1.community <> n2.community WITH n1.community AS c1, n2.community AS c2, COUNT(r) AS weight MATCH (s1:SuperNode {id: c1}), (s2:SuperNode {id: c2}) CREATE (s1)-[:CONNECTED {weight: weight}]->(s2); </code></pre></div>Improvements over Louvain: <ul> <li>Guarantees connectivity within communities</li> <li>Better quality on large graphs</li> <li>Faster convergence</li> </ul> <h4 id="overlapping-community-detection-slpa" class="position-relative d-flex align-items-center group"> Overlapping Community Detection (SLPA) <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="overlapping-community-detection-slpa" aria-haspopup="dialog" aria-label="Share link: Overlapping Community Detection (SLPA)"> Share link </button> </h4>Speaker-Listener Label Propagation Algorithm allows nodes in multiple communities: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Initialize: Each node remembers labels it hears MATCH (n:Node) SET n.memory = [ID(n)]; -- Iterations: Listen, speak, update MATCH (n:Node)-[:CONNECTED]-(neighbor:Node) WITH n, neighbor.memory AS neighbor_labels WITH n, REDUCE(counts = {}, label IN FLATTEN(COLLECT(neighbor_labels)) | CASE WHEN label IN keys(counts) THEN counts + {label: counts[label] + 1} ELSE counts + {label: 1} END ) AS label_counts WITH n, label_counts, [label IN keys(label_counts) ORDER BY label_counts[label] DESC][0] AS most_heard SET n.memory = n.memory + [most_heard]; -- Post-processing: Extract communities MATCH (n:Node) WITH n, REDUCE(freq = {}, label IN n.memory | CASE WHEN label IN keys(freq) THEN freq + {label: freq[label] + 1} ELSE freq + {label: 1} END ) AS label_frequency WITH n, [label IN keys(label_frequency) WHERE label_frequency[label] > SIZE(n.memory) * 0.2] AS communities SET n.communities = communities; -- Query overlapping memberships MATCH (n:Node) WHERE SIZE(n.communities) > 1 RETURN n.id, n.communities, SIZE(n.communities) AS community_count ORDER BY community_count DESC; </code></pre></div>Use cases: Social networks (people in multiple friend groups), protein complexes, topic categorization <h3 id="advanced-quality-metrics" class="position-relative d-flex align-items-center group"> Advanced Quality Metrics <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="advanced-quality-metrics" aria-haspopup="dialog" aria-label="Share link: Advanced Quality Metrics"> Share link </button> </h3> <h4 id="modularity-calculation" class="position-relative d-flex align-items-center group"> Modularity Calculation <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="modularity-calculation" aria-haspopup="dialog" aria-label="Share link: Modularity Calculation"> Share link </button> </h4>Measure community quality: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Compute modularity Q MATCH ()-[r:CONNECTED]-() WITH COUNT(r) / 2.0 AS m MATCH (n:Node) WITH m, n.community AS comm, SUM(SIZE((n)-[:CONNECTED]-())) AS k_sum MATCH (n1:Node)-[r:CONNECTED]-(n2:Node) WHERE n1.community = n2.community WITH m, comm, k_sum, COUNT(r) / 2.0 AS e_in RETURN SUM(e_in / m - (k_sum / (2 * m)) ^ 2) AS modularity; </code></pre></div>Modularity Q: <ul> <li>Q > 0.3: Significant community structure</li> <li>Q > 0.7: Strong communities</li> <li>Q ≈ 0: Random structure</li> </ul> <h4 id="conductance-community-separability" class="position-relative d-flex align-items-center group"> Conductance (Community Separability) <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="conductance-community-separability" aria-haspopup="dialog" aria-label="Share link: Conductance (Community Separability)"> Share link </button> </h4>Measure how well-separated communities are: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Conductance: ratio of external to total edges MATCH (n:Node {community: $community_id}) WITH COLLECT(n) AS community_nodes MATCH (internal:Node)-[r_internal:CONNECTED]-(other:Node) WHERE internal IN community_nodes AND other IN community_nodes WITH community_nodes, COUNT(r_internal) AS internal_edges MATCH (boundary:Node)-[r_boundary:CONNECTED]-(external:Node) WHERE boundary IN community_nodes AND NOT external IN community_nodes WITH internal_edges, COUNT(r_boundary) AS boundary_edges RETURN boundary_edges * 1.0 / (internal_edges + boundary_edges) AS conductance; </code></pre></div>Conductance φ: <ul> <li>φ < 0.2: Well-separated community</li> <li>φ > 0.5: Poorly defined boundary</li> </ul> <h4 id="clustering-coefficient-distribution" class="position-relative d-flex align-items-center group"> Clustering Coefficient Distribution <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="clustering-coefficient-distribution" aria-haspopup="dialog" aria-label="Share link: Clustering Coefficient Distribution"> Share link </button> </h4>Analyze local vs global structure: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Local clustering coefficient MATCH (n:Node)-[:CONNECTED]-(neighbor:Node) WITH n, COLLECT(DISTINCT neighbor) AS neighbors, SIZE((n)-[:CONNECTED]-()) AS degree WHERE degree >= 2 UNWIND neighbors AS n1 UNWIND neighbors AS n2 MATCH (n1)-[r:CONNECTED]-(n2) WHERE n1 < n2 WITH n, degree, COUNT(DISTINCT r) AS connected_pairs RETURN n.id, connected_pairs * 2.0 / (degree * (degree - 1)) AS clustering_coefficient, degree; -- Average clustering by community MATCH (n:Node) WITH n.community AS comm, AVG(n.clustering_coefficient) AS avg_clustering, COUNT(n) AS size RETURN comm, avg_clustering, size ORDER BY avg_clustering DESC; </code></pre></div> <h3 id="real-world-applications" class="position-relative d-flex align-items-center group"> Real-World Applications <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="real-world-applications" aria-haspopup="dialog" aria-label="Share link: Real-World Applications"> Share link </button> </h3> <h4 id="social-network-analysis" class="position-relative d-flex align-items-center group"> Social Network Analysis <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="social-network-analysis" aria-haspopup="dialog" aria-label="Share link: Social Network Analysis"> Share link </button> </h4>Detect friend groups and influential communities: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Identify cohesive friend groups MATCH (u:User) SET u.friend_group = ID(u); MATCH (u:User)-[f:FRIENDS_WITH]-(friend:User) WITH u, friend.friend_group AS group, COUNT(*) AS mutual_connections ORDER BY mutual_connections DESC WITH u, COLLECT(group)[0] AS primary_group SET u.friend_group = primary_group; -- Find community influencers MATCH (influencer:User) WITH influencer.friend_group AS group, influencer, SIZE((influencer)-[:FRIENDS_WITH]-(:User {friend_group: group})) AS internal_connections, SIZE((influencer)-[:FRIENDS_WITH]-(:User)) AS total_connections WHERE internal_connections * 1.0 / total_connections > 0.7 MATCH (influencer)<-[:FOLLOWS]-(follower:User) WHERE follower.friend_group = group WITH group, influencer, COUNT(follower) AS group_followers ORDER BY group_followers DESC RETURN group, influencer.username, group_followers, 'Community Influencer' AS role; </code></pre></div> <h4 id="customer-segmentation" class="position-relative d-flex align-items-center group"> Customer Segmentation <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="customer-segmentation" aria-haspopup="dialog" aria-label="Share link: Customer Segmentation"> Share link </button> </h4>Group customers by purchase behavior: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Product-based customer clustering MATCH (c:Customer)-[:PURCHASED]->(p:Product) WITH c, COLLECT(p.category) AS purchase_categories SET c.category_vector = purchase_categories; MATCH (c1:Customer)-[:PURCHASED]->(common:Product)<-[:PURCHASED]-(c2:Customer) WHERE ID(c1) < ID(c2) WITH c1, c2, COUNT(DISTINCT common) AS common_purchases WHERE common_purchases >= 5 MERGE (c1)-[:SIMILAR_CUSTOMER {similarity: common_purchases}]-(c2); -- Label propagation for segments MATCH (c:Customer) SET c.segment = ID(c); MATCH (c:Customer)-[s:SIMILAR_CUSTOMER]-(other:Customer) WITH c, other.segment AS segment, SUM(s.similarity) AS total_similarity ORDER BY total_similarity DESC WITH c, COLLECT(segment)[0] AS dominant_segment SET c.segment = dominant_segment; -- Analyze segment characteristics MATCH (c:Customer) WITH c.segment AS segment, AVG(c.lifetime_value) AS avg_ltv, AVG(c.purchase_frequency) AS avg_frequency, COUNT(c) AS segment_size RETURN segment, avg_ltv, avg_frequency, segment_size ORDER BY avg_ltv DESC; </code></pre></div> <h4 id="network-infrastructure-analysis" class="position-relative d-flex align-items-center group"> Network Infrastructure Analysis <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="network-infrastructure-analysis" aria-haspopup="dialog" aria-label="Share link: Network Infrastructure Analysis"> Share link </button> </h4>Detect network clusters and failure domains: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Identify network zones MATCH (node:NetworkNode) SET node.zone = ID(node); MATCH (n1:NetworkNode)-[link:CONNECTED]-(n2:NetworkNode) WHERE link.latency_ms < 10 // Low latency = same zone WITH n1, n2.zone AS candidate_zone, COUNT(*) AS connections ORDER BY connections DESC WITH n1, COLLECT(candidate_zone)[0] AS primary_zone SET n1.zone = primary_zone; -- Find critical inter-zone links MATCH (n1:NetworkNode)-[link:CONNECTED]-(n2:NetworkNode) WHERE n1.zone <> n2.zone WITH n1.zone AS zone1, n2.zone AS zone2, COUNT(link) AS interconnect_count, MIN(link.bandwidth_gbps) AS min_bandwidth WHERE interconnect_count < 3 // Potential bottleneck RETURN zone1, zone2, interconnect_count, min_bandwidth, 'CRITICAL_LINK' AS alert_level; </code></pre></div> <h3 id="performance-tuning" class="position-relative d-flex align-items-center group"> Performance Tuning <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="performance-tuning" aria-haspopup="dialog" aria-label="Share link: Performance Tuning"> Share link </button> </h3> <h4 id="algorithm-complexity-analysis" class="position-relative d-flex align-items-center group"> Algorithm Complexity Analysis <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="algorithm-complexity-analysis" aria-haspopup="dialog" aria-label="Share link: Algorithm Complexity Analysis"> Share link </button> </h4>Label Propagation: <ul> <li>Time: O(k × E) where k = iterations (typically 10-50)</li> <li>Space: O(V) for label storage</li> <li>Parallelizable: Yes (synchronous updates)</li> </ul> Louvain Method: <ul> <li>Time: O(V × log V) expected</li> <li>Space: O(V + E)</li> <li>Levels: Typically 3-5 for real networks</li> </ul> Connected Components: <ul> <li>Time: O(V + E) with Union-Find</li> <li>Space: O(V)</li> <li>Parallelizable: Yes (with caution)</li> </ul> <h4 id="large-scale-optimization" class="position-relative d-flex align-items-center group"> Large-Scale Optimization <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="large-scale-optimization" aria-haspopup="dialog" aria-label="Share link: Large-Scale Optimization"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Distributed label propagation MATCH (n:Node) WITH n, ID(n) % $num_partitions AS partition CALL { WITH n, partition MATCH (n)-[:CONNECTED]-(neighbor:Node) WITH n, neighbor.community AS label, COUNT(*) AS freq ORDER BY freq DESC LIMIT 1 SET n.community_new = label } IN TRANSACTIONS OF 100000 ROWS PER PARTITION (partition); -- Approximate community detection for billion-node graphs WITH 0.01 AS sample_rate // Sample 1% of nodes MATCH (n:Node) WHERE rand() < sample_rate SET n.sampled = true; // Detect communities on sample MATCH (s:Node {sampled: true})-[:CONNECTED*1..2]-(neighbor:Node {sampled: true}) // Run standard algorithm on sample... // Propagate to full graph MATCH (full:Node) WHERE full.sampled IS NULL MATCH (full)-[:CONNECTED]-(sampled:Node {sampled: true}) WITH full, sampled.community AS comm, COUNT(*) AS connections ORDER BY connections DESC LIMIT 1 SET full.community = comm; </code></pre></div> <h3 id="validation-and-quality-assurance" class="position-relative d-flex align-items-center group"> Validation and Quality Assurance <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="validation-and-quality-assurance" aria-haspopup="dialog" aria-label="Share link: Validation and Quality Assurance"> Share link </button> </h3> <h4 id="ground-truth-comparison" class="position-relative d-flex align-items-center group"> Ground Truth Comparison <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="ground-truth-comparison" aria-haspopup="dialog" aria-label="Share link: Ground Truth Comparison"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Compare detected communities to known structure MATCH (n:Node) WHERE n.true_community IS NOT NULL AND n.detected_community IS NOT NULL WITH n.true_community AS true_comm, n.detected_community AS detected_comm, COUNT(n) AS overlap WITH true_comm, detected_comm, MAX(overlap) AS max_overlap WITH SUM(max_overlap) AS total_correct, COUNT { MATCH (n:Node) } AS total_nodes RETURN total_correct * 1.0 / total_nodes AS accuracy; -- Adjusted Rand Index (ARI) // Measures agreement between two partitions // ARI = 1: Perfect agreement // ARI = 0: Random agreement // ARI < 0: Less than random </code></pre></div> <h4 id="stability-analysis" class="position-relative d-flex align-items-center group"> Stability Analysis <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="stability-analysis" aria-haspopup="dialog" aria-label="Share link: Stability Analysis"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Test community stability across algorithm runs MATCH (n:Node) SET n.run1_community = n.community; // Re-run algorithm with slight perturbation... MATCH (n:Node) WITH COUNT(CASE WHEN n.run1_community = n.run2_community THEN 1 END) AS stable, COUNT(n) AS total RETURN stable * 100.0 / total AS stability_percent; </code></pre></div> <h3 id="related-topics" class="position-relative d-flex align-items-center group"> Related Topics <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="related-topics" aria-haspopup="dialog" aria-label="Share link: Related Topics"> Share link </button> </h3><ul> <li>Graph Algorithms: See graph-algorithms tag for algorithm implementations</li> <li>PageRank: Use pagerank for node importance within communities</li> <li>Pattern Matching: Check patterns tag for community traversal queries</li> <li>Analytics: Explore analytics tag for community analysis techniques</li> <li>Clustering: Explore clustering techniques and quality metrics</li> <li>Network Analysis: Social network analysis and influence detection</li> <li>Graph Partitioning: Balanced graph cuts and partitioning algorithms</li> </ul> <h3 id="further-reading" class="position-relative d-flex align-items-center group"> Further Reading <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="further-reading" aria-haspopup="dialog" aria-label="Share link: Further Reading"> Share link </button> </h3><ul> <li>Community Detection Algorithms: Comparative Analysis and Benchmarks</li> <li>Modularity Optimization: Theory and Practice</li> <li>Overlapping Communities: Detection and Interpretation</li> <li>Hierarchical Clustering: Multi-Scale Community Structure</li> <li>Large-Scale Community Detection: Distributed and Streaming Algorithms</li> <li>Quality Metrics: Modularity, Conductance, and NMI</li> <li>Applications: Social Networks, Biology, and Infrastructure</li> </ul> Browse the tagged content below to discover documentation, tutorials, and guides for implementing community detection in your Geode applications.

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