Graph Analytics Algorithms

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Unlike traditional analytics that focus on individual records, graph analytics leverages relationships to uncover hidden patterns, identify influential nodes, detect communities, and measure network properties. Geode provides powerful graph traversal capabilities through GQL, enabling implementation of classic graph algorithms directly in your queries. This guide covers centrality measures, community detection, path analysis, similarity metrics, and practical applications. <h3 id="centrality-algorithms" class="position-relative d-flex align-items-center group"> Centrality Algorithms <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="centrality-algorithms" aria-haspopup="dialog" aria-label="Share link: Centrality Algorithms"> Share link </button> </h3>Centrality algorithms identify the most important or influential nodes in a graph based on their position and connections. <h4 id="degree-centrality" class="position-relative d-flex align-items-center group"> Degree Centrality <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="degree-centrality" aria-haspopup="dialog" aria-label="Share link: Degree Centrality"> Share link </button> </h4>The simplest centrality measure counts the number of connections a node has. <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Calculate in-degree (incoming connections) MATCH (n:User) OPTIONAL MATCH (n)<-[r:FOLLOWS]-() WITH n, COUNT(r) AS in_degree RETURN n.name, in_degree ORDER BY in_degree DESC LIMIT 20; -- Calculate out-degree (outgoing connections) MATCH (n:User) OPTIONAL MATCH (n)-[r:FOLLOWS]->() WITH n, COUNT(r) AS out_degree RETURN n.name, out_degree ORDER BY out_degree DESC; -- Total degree (both directions) MATCH (n:User) OPTIONAL MATCH (n)-[r:FOLLOWS]-() WITH n, COUNT(r) AS total_degree RETURN n.name, total_degree ORDER BY total_degree DESC; -- Store degree centrality on nodes MATCH (n:User) SET n.in_degree = COUNT { (n)<-[:FOLLOWS]-() }, n.out_degree = COUNT { (n)-[:FOLLOWS]->() }; </code></pre></div> <h4 id="pagerank" class="position-relative d-flex align-items-center group"> PageRank <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="pagerank" aria-haspopup="dialog" aria-label="Share link: PageRank"> Share link </button> </h4>PageRank measures node importance based on the quality and quantity of incoming links. <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Initialize PageRank scores MATCH (n:Page) WITH COUNT(n) AS total_nodes MATCH (n:Page) SET n.pagerank = 1.0 / total_nodes; -- Iterative PageRank calculation (run 20+ times) MATCH (source:Page)-[:LINKS_TO]->(target:Page) WITH target, SUM(source.pagerank / COUNT { (source)-[:LINKS_TO]->() }) AS rank_contribution SET target.pagerank_new = 0.15 + 0.85 * rank_contribution; -- Apply updates MATCH (n:Page) SET n.pagerank = COALESCE(n.pagerank_new, 0.15), n.pagerank_new = null; -- Get top-ranked pages MATCH (p:Page) RETURN p.url, p.title, p.pagerank ORDER BY p.pagerank DESC LIMIT 25; </code></pre></div> <h4 id="betweenness-centrality" class="position-relative d-flex align-items-center group"> Betweenness Centrality <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="betweenness-centrality" aria-haspopup="dialog" aria-label="Share link: Betweenness Centrality"> Share link </button> </h4>Betweenness centrality measures how often a node lies on the shortest path between other nodes. <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Simplified betweenness (for small graphs) -- Count paths through each node MATCH (source:Person), (target:Person) WHERE source <> target MATCH path = shortestPath((source)-[:KNOWS*..10]->(target)) UNWIND nodes(path) AS intermediate WHERE intermediate <> source AND intermediate <> target WITH intermediate, COUNT(*) AS path_count RETURN intermediate.name, path_count AS betweenness_score ORDER BY betweenness_score DESC; -- Approximate betweenness using sampling MATCH (sample:Person) WHERE rand() < 0.1 -- Sample 10% of nodes WITH COLLECT(sample) AS sources UNWIND sources AS source MATCH (target:Person) WHERE source <> target AND rand() < 0.1 MATCH path = shortestPath((source)-[:KNOWS*..6]->(target)) UNWIND nodes(path) AS intermediate WHERE intermediate <> source AND intermediate <> target WITH intermediate, COUNT(*) AS sampled_paths RETURN intermediate.name, sampled_paths * 100 AS estimated_betweenness -- Scale up ORDER BY estimated_betweenness DESC LIMIT 20; </code></pre></div> <h4 id="closeness-centrality" class="position-relative d-flex align-items-center group"> Closeness Centrality <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="closeness-centrality" aria-haspopup="dialog" aria-label="Share link: Closeness Centrality"> Share link </button> </h4>Closeness centrality measures how close a node is to all other nodes in the network. <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Calculate average shortest path length from each node MATCH (n:Person) MATCH (other:Person) WHERE n <> other MATCH path = shortestPath((n)-[:KNOWS*..10]->(other)) WITH n, AVG(length(path)) AS avg_distance SET n.closeness = 1.0 / avg_distance; -- Query closeness rankings MATCH (p:Person) WHERE p.closeness IS NOT NULL RETURN p.name, p.closeness ORDER BY p.closeness DESC LIMIT 20; -- Harmonic closeness (handles disconnected graphs) MATCH (n:Person) MATCH (other:Person) WHERE n <> other OPTIONAL MATCH path = shortestPath((n)-[:KNOWS*..10]->(other)) WITH n, SUM(CASE WHEN path IS NOT NULL THEN 1.0 / length(path) ELSE 0 END) AS harmonic_sum SET n.harmonic_closeness = harmonic_sum; </code></pre></div> <h4 id="eigenvector-centrality" class="position-relative d-flex align-items-center group"> Eigenvector Centrality <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="eigenvector-centrality" aria-haspopup="dialog" aria-label="Share link: Eigenvector Centrality"> Share link </button> </h4>Eigenvector centrality considers both the number of connections and the importance of connected nodes. <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Initialize scores MATCH (n:User) SET n.eigenvector = 1.0; -- Iterative calculation (run until convergence) MATCH (n:User)<-[:FOLLOWS]-(neighbor:User) WITH n, SUM(neighbor.eigenvector) AS neighbor_sum SET n.eigenvector_new = neighbor_sum; -- Normalize MATCH (n:User) WITH SQRT(SUM(n.eigenvector_new * n.eigenvector_new)) AS norm MATCH (n:User) SET n.eigenvector = n.eigenvector_new / norm, n.eigenvector_new = null; -- Top nodes by eigenvector centrality MATCH (u:User) RETURN u.name, u.eigenvector ORDER BY u.eigenvector DESC LIMIT 20; </code></pre></div> <h3 id="community-detection" class="position-relative d-flex align-items-center group"> 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="community-detection" aria-haspopup="dialog" aria-label="Share link: Community Detection"> Share link </button> </h3>Community detection algorithms identify groups of densely connected nodes. <h4 id="label-propagation" class="position-relative d-flex align-items-center group"> 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="label-propagation" aria-haspopup="dialog" aria-label="Share link: Label Propagation"> Share link </button> </h4>Nodes adopt the most common label among their neighbors. <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Initialize with unique community IDs MATCH (n:User) SET n.community = id(n); -- Propagate labels (run until stable) MATCH (n:User)-[:KNOWS]-(neighbor:User) WITH n, neighbor.community AS neighbor_community WITH n, neighbor_community, COUNT(*) AS frequency ORDER BY n, frequency DESC WITH n, COLLECT(neighbor_community)[0] AS dominant_community SET n.community_new = dominant_community; -- Apply updates MATCH (n:User) SET n.community = n.community_new, n.community_new = null; -- View communities MATCH (n:User) RETURN n.community AS community_id, COUNT(n) AS member_count, COLLECT(n.name) AS members ORDER BY member_count DESC; </code></pre></div> <h4 id="louvain-modularity" class="position-relative d-flex align-items-center group"> Louvain 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="louvain-modularity" aria-haspopup="dialog" aria-label="Share link: Louvain Modularity"> Share link </button> </h4>Optimizes modularity by moving nodes between communities. <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Initialize: each node in its own community MATCH (n:User) SET n.community = id(n); -- Calculate initial modularity contribution MATCH (n:User) WITH n, COUNT { (n)-[:KNOWS]-() } AS degree SET n.degree = degree; -- Phase 1: Local moving (simplified) MATCH (n:User)-[:KNOWS]-(neighbor:User) WHERE n.community <> neighbor.community WITH n, neighbor.community AS neighbor_comm, COUNT(*) AS edges_to_comm ORDER BY edges_to_comm DESC WITH n, COLLECT(neighbor_comm)[0] AS best_community WHERE edges_to_comm > 0 SET n.community = best_community; -- Count communities and sizes MATCH (n:User) RETURN n.community AS community, COUNT(n) AS size ORDER BY size DESC; </code></pre></div> <h4 id="triangle-counting-and-clustering-coefficient" class="position-relative d-flex align-items-center group"> Triangle Counting and Clustering Coefficient <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="triangle-counting-and-clustering-coefficient" aria-haspopup="dialog" aria-label="Share link: Triangle Counting and Clustering Coefficient"> Share link </button> </h4>Measures how interconnected a node’s neighbors are. <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Count triangles involving each node MATCH (a:User)-[:KNOWS]->(b:User)-[:KNOWS]->(c:User)-[:KNOWS]->(a) WHERE id(a) < id(b) AND id(b) < id(c) RETURN a.name, COUNT(*) AS triangle_count ORDER BY triangle_count DESC; -- Calculate local clustering coefficient MATCH (n:User) WITH n, COUNT { (n)-[:KNOWS]-() } AS degree WHERE degree >= 2 MATCH (n)-[:KNOWS]-(neighbor1:User) MATCH (n)-[:KNOWS]-(neighbor2:User) WHERE id(neighbor1) < id(neighbor2) OPTIONAL MATCH (neighbor1)-[conn:KNOWS]-(neighbor2) WITH n, degree, COUNT(conn) AS connected_neighbors WITH n, degree, connected_neighbors * 2.0 / (degree * (degree - 1)) AS clustering_coef SET n.clustering_coefficient = clustering_coef; -- Global clustering coefficient MATCH (a:User)-[:KNOWS]->(b:User)-[:KNOWS]->(c:User) WHERE a <> c WITH COUNT(*) AS paths_of_2 MATCH (a:User)-[:KNOWS]->(b:User)-[:KNOWS]->(c:User)-[:KNOWS]->(a) WHERE id(a) < id(b) AND id(b) < id(c) WITH paths_of_2, COUNT(*) * 6 AS triangles RETURN triangles * 1.0 / paths_of_2 AS global_clustering; </code></pre></div> <h3 id="path-analysis" class="position-relative d-flex align-items-center group"> Path 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="path-analysis" aria-haspopup="dialog" aria-label="Share link: Path Analysis"> Share link </button> </h3> <h4 id="shortest-path" class="position-relative d-flex align-items-center group"> Shortest Path <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="shortest-path" aria-haspopup="dialog" aria-label="Share link: Shortest Path"> Share link </button> </h4>Find the shortest path between nodes. <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Single shortest path MATCH path = shortestPath( (start:User {name: 'Alice'})-[:KNOWS*..10]->(end:User {name: 'Bob'}) ) RETURN [n IN nodes(path) | n.name] AS path, length(path) AS distance; -- All shortest paths (same length) MATCH path = allShortestPaths( (start:User {name: 'Alice'})-[:KNOWS*..10]->(end:User {name: 'Bob'}) ) RETURN [n IN nodes(path) | n.name] AS path; -- Weighted shortest path MATCH path = shortestPath( (start:City {name: 'Austin'})-[:ROAD*..20]->(end:City {name: 'Seattle'}) ) WITH path, REDUCE(total = 0, r IN relationships(path) | total + r.distance) AS total_distance RETURN [n IN nodes(path) | n.name] AS route, total_distance ORDER BY total_distance LIMIT 1; </code></pre></div> <h4 id="path-finding-with-constraints" class="position-relative d-flex align-items-center group"> Path Finding with Constraints <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="path-finding-with-constraints" aria-haspopup="dialog" aria-label="Share link: Path Finding with Constraints"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Find paths avoiding certain nodes MATCH path = (start:User {name: 'Alice'})-[:KNOWS*2..5]->(end:User {name: 'Charlie'}) WHERE NONE(n IN nodes(path) WHERE n.name = 'Eve') RETURN [n IN nodes(path) | n.name] AS path LIMIT 10; -- Find paths through specific intermediate nodes MATCH (start:User {name: 'Alice'}) MATCH (waypoint:User {name: 'Bob'}) MATCH (end:User {name: 'Charlie'}) MATCH path1 = shortestPath((start)-[:KNOWS*..5]->(waypoint)) MATCH path2 = shortestPath((waypoint)-[:KNOWS*..5]->(end)) RETURN [n IN nodes(path1) | n.name] + [n IN nodes(path2)[1..] | n.name] AS full_path; -- Find paths with property constraints MATCH path = (start:User {name: 'Alice'})-[:KNOWS*2..4]->(end:User) WHERE ALL(r IN relationships(path) WHERE r.trust_level > 0.5) RETURN end.name, length(path) AS distance; </code></pre></div> <h4 id="k-hop-neighbors" class="position-relative d-flex align-items-center group"> K-Hop Neighbors <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="k-hop-neighbors" aria-haspopup="dialog" aria-label="Share link: K-Hop Neighbors"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Find all users within k hops MATCH (start:User {name: 'Alice'})-[:KNOWS*1..3]->(neighbor:User) WHERE neighbor <> start RETURN DISTINCT neighbor.name, MIN(length(path)) AS min_distance; -- Count neighbors at each distance MATCH (start:User {name: 'Alice'}) UNWIND range(1, 5) AS distance OPTIONAL MATCH path = (start)-[:KNOWS*]->(neighbor) WHERE length(path) = distance AND neighbor <> start WITH distance, COUNT(DISTINCT neighbor) AS neighbors_at_distance RETURN distance, neighbors_at_distance; </code></pre></div> <h3 id="similarity-metrics" class="position-relative d-flex align-items-center group"> Similarity 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="similarity-metrics" aria-haspopup="dialog" aria-label="Share link: Similarity Metrics"> Share link </button> </h3> <h4 id="jaccard-similarity" class="position-relative d-flex align-items-center group"> Jaccard Similarity <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="jaccard-similarity" aria-haspopup="dialog" aria-label="Share link: Jaccard Similarity"> Share link </button> </h4>Measures overlap between neighborhoods. <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Jaccard similarity between two users MATCH (u1:User {name: 'Alice'})-[:KNOWS]->(friend1:User) MATCH (u2:User {name: 'Bob'})-[:KNOWS]->(friend2:User) WITH u1, u2, COLLECT(DISTINCT friend1) AS friends1, COLLECT(DISTINCT friend2) AS friends2 WITH u1, u2, SIZE([f IN friends1 WHERE f IN friends2]) AS intersection, SIZE(friends1) + SIZE(friends2) AS union_size RETURN u1.name, u2.name, intersection * 1.0 / (union_size - intersection) AS jaccard_similarity; -- Find similar users to a given user MATCH (target:User {name: 'Alice'})-[:KNOWS]->(target_friend:User) WITH target, COLLECT(DISTINCT target_friend) AS target_friends MATCH (other:User)-[:KNOWS]->(other_friend:User) WHERE other <> target WITH target, target_friends, other, COLLECT(DISTINCT other_friend) AS other_friends WITH target, other, SIZE([f IN target_friends WHERE f IN other_friends]) AS shared, SIZE(target_friends) AS t_size, SIZE(other_friends) AS o_size WHERE shared > 0 RETURN other.name, shared * 1.0 / (t_size + o_size - shared) AS similarity ORDER BY similarity DESC LIMIT 10; </code></pre></div> <h4 id="cosine-similarity" class="position-relative d-flex align-items-center group"> Cosine Similarity <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="cosine-similarity" aria-haspopup="dialog" aria-label="Share link: Cosine Similarity"> Share link </button> </h4>For weighted relationships or feature vectors. <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Cosine similarity based on common interests MATCH (u1:User {name: 'Alice'})-[r1:INTERESTED_IN]->(topic:Topic) MATCH (u2:User {name: 'Bob'})-[r2:INTERESTED_IN]->(topic) WITH u1, u2, SUM(r1.weight * r2.weight) AS dot_product MATCH (u1)-[r:INTERESTED_IN]->() WITH u1, u2, dot_product, SQRT(SUM(r.weight * r.weight)) AS norm1 MATCH (u2)-[r:INTERESTED_IN]->() WITH u1, u2, dot_product, norm1, SQRT(SUM(r.weight * r.weight)) AS norm2 RETURN u1.name, u2.name, dot_product / (norm1 * norm2) AS cosine_similarity; </code></pre></div> <h4 id="adamic-adar-index" class="position-relative d-flex align-items-center group"> Adamic-Adar Index <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="adamic-adar-index" aria-haspopup="dialog" aria-label="Share link: Adamic-Adar Index"> Share link </button> </h4>Weights common neighbors by their rarity. <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Adamic-Adar similarity MATCH (u1:User {name: 'Alice'})-[:KNOWS]->(common:User)<-[:KNOWS]-(u2:User {name: 'Bob'}) WITH u1, u2, common, COUNT { (common)-[:KNOWS]-() } AS common_degree WHERE common_degree > 1 RETURN u1.name, u2.name, SUM(1.0 / log(common_degree)) AS adamic_adar_score; -- Link prediction using Adamic-Adar MATCH (u:User {name: 'Alice'})-[:KNOWS]->(common:User)<-[:KNOWS]-(candidate:User) WHERE NOT (u)-[:KNOWS]-(candidate) AND u <> candidate WITH u, candidate, common, COUNT { (common)-[:KNOWS]-() } AS common_degree WHERE common_degree > 1 WITH u, candidate, SUM(1.0 / log(common_degree)) AS score RETURN candidate.name, score ORDER BY score DESC LIMIT 10; </code></pre></div> <h3 id="network-metrics" class="position-relative d-flex align-items-center group"> Network 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="network-metrics" aria-haspopup="dialog" aria-label="Share link: Network Metrics"> Share link </button> </h3> <h4 id="graph-density" class="position-relative d-flex align-items-center group"> Graph Density <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="graph-density" aria-haspopup="dialog" aria-label="Share link: Graph Density"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Calculate graph density MATCH (n:User) WITH COUNT(n) AS node_count MATCH ()-[r:KNOWS]->() WITH node_count, COUNT(r) AS edge_count RETURN edge_count * 1.0 / (node_count * (node_count - 1)) AS density; -- Density for undirected interpretation MATCH (n:User) WITH COUNT(n) AS node_count MATCH ()-[r:KNOWS]-() WITH node_count, COUNT(r) / 2 AS edge_count RETURN edge_count * 2.0 / (node_count * (node_count - 1)) AS undirected_density; </code></pre></div> <h4 id="diameter-and-radius" class="position-relative d-flex align-items-center group"> Diameter and Radius <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="diameter-and-radius" aria-haspopup="dialog" aria-label="Share link: Diameter and Radius"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Approximate diameter (longest shortest path) MATCH (n:User) WHERE rand() < 0.1 -- Sample nodes WITH COLLECT(n) AS samples UNWIND samples AS source UNWIND samples AS target WHERE source <> target MATCH path = shortestPath((source)-[:KNOWS*..20]->(target)) WITH MAX(length(path)) AS diameter RETURN diameter; -- Eccentricity of specific node MATCH (center:User {name: 'Alice'}) MATCH (other:User) WHERE center <> other MATCH path = shortestPath((center)-[:KNOWS*..20]->(other)) WITH MAX(length(path)) AS eccentricity RETURN eccentricity; </code></pre></div> <h4 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> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Find weakly connected components MATCH (n:User) SET n.component = id(n); -- Propagate minimum ID (repeat until stable) MATCH (n:User)-[:KNOWS]-(neighbor:User) WITH n, MIN(neighbor.component) AS min_neighbor_component WHERE min_neighbor_component < n.component SET n.component = min_neighbor_component; -- Count components MATCH (n:User) RETURN n.component AS component, COUNT(n) AS size ORDER BY size DESC; -- Find nodes in largest component MATCH (n:User) WITH n.component AS comp, COUNT(n) AS size ORDER BY size DESC LIMIT 1 MATCH (member:User {component: comp}) RETURN member.name; </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="fraud-detection" class="position-relative d-flex align-items-center group"> Fraud 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="fraud-detection" aria-haspopup="dialog" aria-label="Share link: Fraud Detection"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Identify suspicious transaction clusters MATCH (a:Account)-[t:TRANSFERRED]->(b:Account) WHERE t.amount > 10000 AND t.timestamp >= datetime() - DURATION 'P7D' WITH a, b, SUM(t.amount) AS total_transferred WHERE total_transferred > 50000 MATCH path = (a)-[:TRANSFERRED*1..3]->(c:Account) WITH COLLECT(DISTINCT a) + COLLECT(DISTINCT b) + COLLECT(DISTINCT c) AS suspects UNWIND suspects AS suspect RETURN DISTINCT suspect.account_number, suspect.holder_name, COUNT { (suspect)-[:TRANSFERRED]-() } AS transaction_count; -- Ring detection MATCH path = (a:Account)-[:TRANSFERRED*3..6]->(a) WHERE ALL(t IN relationships(path) WHERE t.amount > 5000) RETURN [n IN nodes(path) | n.account_number] AS ring, REDUCE(total = 0, t IN relationships(path) | total + t.amount) AS ring_volume; </code></pre></div> <h4 id="recommendation-engine" class="position-relative d-flex align-items-center group"> Recommendation Engine <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="recommendation-engine" aria-haspopup="dialog" aria-label="Share link: Recommendation Engine"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Collaborative filtering: users who liked similar items MATCH (target:User {id: $user_id})-[:LIKED]->(item:Product) MATCH (similar:User)-[:LIKED]->(item) WHERE similar <> target WITH similar, COUNT(item) AS shared_likes ORDER BY shared_likes DESC LIMIT 50 MATCH (similar)-[:LIKED]->(rec:Product) WHERE NOT (target)-[:LIKED]->(rec) RETURN rec.name, rec.id, COUNT(similar) AS recommenders, AVG(similar.shared_likes) AS avg_similarity ORDER BY recommenders DESC, avg_similarity DESC LIMIT 20; -- Content-based with graph structure MATCH (target:User {id: $user_id})-[:LIKED]->(liked:Product) MATCH (liked)-[:IN_CATEGORY]->(cat:Category) MATCH (rec:Product)-[:IN_CATEGORY]->(cat) WHERE NOT (target)-[:LIKED]->(rec) RETURN rec.name, COUNT(DISTINCT cat) AS category_matches, COLLECT(DISTINCT cat.name) AS matching_categories ORDER BY category_matches DESC LIMIT 20; </code></pre></div> <h4 id="influence-analysis" class="position-relative d-flex align-items-center group"> Influence 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="influence-analysis" aria-haspopup="dialog" aria-label="Share link: Influence Analysis"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Find influencers in network MATCH (u:User) WITH u, COUNT { (u)<-[:FOLLOWS]-() } AS followers, COUNT { (u)-[:FOLLOWS]->() } AS following WHERE followers > 0 WITH u, followers, following, followers * 1.0 / (following + 1) AS influence_ratio WHERE influence_ratio > 5 RETURN u.name, followers, following, influence_ratio ORDER BY followers DESC LIMIT 50; -- Measure reach (followers of followers) MATCH (influencer:User {name: $name})<-[:FOLLOWS]-(follower:User) OPTIONAL MATCH (follower)<-[:FOLLOWS]-(fof:User) WITH influencer, COUNT(DISTINCT follower) AS direct_reach, COUNT(DISTINCT fof) AS indirect_reach RETURN influencer.name, direct_reach, indirect_reach, direct_reach + indirect_reach AS total_reach; </code></pre></div> <h4 id="supply-chain-analysis" class="position-relative d-flex align-items-center group"> Supply Chain 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="supply-chain-analysis" aria-haspopup="dialog" aria-label="Share link: Supply Chain Analysis"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Critical path in supply network MATCH path = (supplier:Supplier)-[:SUPPLIES*]->(manufacturer:Manufacturer) WHERE supplier.product = 'Microchip' AND manufacturer.name = 'AutoCorp' WITH path, REDUCE(lead_time = 0, r IN relationships(path) | lead_time + r.lead_days) AS total_lead_time RETURN [n IN nodes(path) | n.name] AS supply_chain, total_lead_time ORDER BY total_lead_time; -- Identify bottlenecks (high betweenness in supply graph) MATCH (n:Supplier) SET n.supply_betweenness = 0; MATCH (source:Supplier), (target:Manufacturer) MATCH path = shortestPath((source)-[:SUPPLIES*..10]->(target)) UNWIND nodes(path) AS intermediate WHERE intermediate:Supplier WITH intermediate, COUNT(*) AS path_count SET intermediate.supply_betweenness = intermediate.supply_betweenness + path_count; MATCH (s:Supplier) RETURN s.name, s.supply_betweenness ORDER BY s.supply_betweenness DESC LIMIT 10; </code></pre></div> <h3 id="client-library-examples" class="position-relative d-flex align-items-center group"> Client Library 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="client-library-examples" aria-haspopup="dialog" aria-label="Share link: Client Library 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 run_analytics(): client = Client(host="localhost", port=3141) async with client.connection() as conn: # Calculate PageRank await conn.execute(""" MATCH (n:Page) SET n.pagerank = 1.0 / COUNT { MATCH (p:Page) } """) # Run 20 iterations for i in range(20): await conn.execute(""" MATCH (source:Page)-[:LINKS_TO]->(target:Page) WITH target, SUM(source.pagerank / COUNT { (source)-[:LINKS_TO]->() }) AS contribution SET target.pagerank_new = 0.15 + 0.85 * contribution """) await conn.execute(""" MATCH (n:Page) SET n.pagerank = COALESCE(n.pagerank_new, 0.15), n.pagerank_new = null """) # Get results result, _ = await conn.query(""" MATCH (p:Page) RETURN p.url, p.pagerank ORDER BY p.pagerank DESC LIMIT 20 """) for row in result.rows: print(f"{row['p.url']}: {row['p.pagerank']:.4f}") </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, Value}; async fn community_detection(client: &Client) -> Result<(), Box<dyn std::error::Error>> { // Initialize communities client.execute( "MATCH (n:User) SET n.community = id(n)", &[], ).await?; // Run label propagation for iteration in 0..10 { let changes = client.query( r#" MATCH (n:User)-[:KNOWS]-(neighbor:User) WITH n, neighbor.community AS nc, COUNT(*) AS freq ORDER BY n, freq DESC WITH n, COLLECT(nc)[0] AS best_community WHERE n.community <> best_community SET n.community = best_community RETURN COUNT(n) AS changes_made "#, &[], ).await?; let change_count: i64 = changes.rows()[0].get("changes_made")?; println!("Iteration {}: {} changes", iteration, change_count); if change_count == 0 { break; } } // Get community sizes let communities = client.query( r#" MATCH (n:User) RETURN n.community AS community, COUNT(n) AS size ORDER BY size DESC "#, &[], ).await?; for row in communities.rows() { println!("Community {}: {} members", row.get::<i64>("community")?, row.get::<i64>("size")? ); } Ok(()) } </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="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> </h4><ul> <li>Index properties used in WHERE clauses</li> <li>Use bounded path lengths (*1..5 instead of *)</li> <li>Sample large graphs for approximate algorithms</li> <li>Pre-compute and store centrality scores</li> <li>Use batch updates for iterative algorithms</li> </ul> <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><ul> <li>Degree centrality: Simple importance measure</li> <li>PageRank: Link-based importance</li> <li>Betweenness: Bridge/broker identification</li> <li>Closeness: Rapid information spread</li> <li>Community detection: Group identification</li> </ul> <h4 id="scalability" class="position-relative d-flex align-items-center group"> Scalability <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="scalability" aria-haspopup="dialog" aria-label="Share link: Scalability"> Share link </button> </h4><ul> <li>For large graphs, use approximate algorithms</li> <li>Consider incremental updates instead of full recomputation</li> <li>Partition graph for parallel processing</li> <li>Cache intermediate results</li> </ul> <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><a href="/tags/pagerank/" >PageRank</a> - PageRank algorithm details</li> <li><a href="/tags/community-detection/" >Community Detection</a> - Clustering algorithms</li> <li><a href="/tags/algorithms/" >Graph Algorithms</a> - General graph algorithms</li> <li><a href="/tags/performance/" >Performance</a> - Query optimization</li> <li><a href="/tags/analytics/" >Analytics</a> - Analytical capabilities</li> <li><a href="/tags/patterns/" >Patterns</a> - Query patterns</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>Graph Algorithm Theory and Applications</li> <li>Network Analysis with Graph Databases</li> <li>Scalable Graph Analytics</li> <li>Centrality Measures Comparison</li> <li>Community Detection Algorithms</li> </ul> Browse tagged content for complete graph analytics documentation and examples.

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