Graph Algorithms

Graph algorithms are specialized computational methods designed to analyze and extract insights from graph-structured data. Geode provides both built-in GQL capabilities and extensibility for implementing advanced graph algorithms on your connected data. <h3 id="what-are-graph-algorithms" class="position-relative d-flex align-items-center group"> What are Graph 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="what-are-graph-algorithms" aria-haspopup="dialog" aria-label="Share link: What are Graph Algorithms?"> Share link </button> </h3><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; 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Unlike traditional table-based computations, graph algorithms excel at: <ul> <li>Pathfinding: Discovering routes and connections between nodes</li> <li>Centrality Analysis: Identifying influential or important nodes</li> <li>Community Detection: Finding clusters of related entities</li> <li>Similarity Computation: Measuring how closely nodes are related</li> <li>Network Flow: Optimizing resource distribution through networks</li> </ul> These algorithms power applications ranging from social network analysis to logistics optimization, fraud detection, and recommendation systems. <h3 id="algorithm-categories" class="position-relative d-flex align-items-center group"> Algorithm Categories <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-categories" aria-haspopup="dialog" aria-label="Share link: Algorithm Categories"> Share link </button> </h3> <h4 id="pathfinding-algorithms" class="position-relative d-flex align-items-center group"> Pathfinding 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="pathfinding-algorithms" aria-haspopup="dialog" aria-label="Share link: Pathfinding Algorithms"> Share link </button> </h4> <h5 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> </h5>Find the shortest path between two nodes: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">// Simple shortest path MATCH path = SHORTEST (a:Person {name: 'Alice'})-[:KNOWS*]->(b:Person {name: 'Bob'}) RETURN path // Weighted shortest path with relationship properties MATCH path = SHORTEST (a:City {name: 'NYC'})-[r:ROAD*]-(b:City {name: 'SF'}) WHERE ALL(rel IN r WHERE rel.distance IS NOT NULL) RETURN path, REDUCE(total = 0, rel IN r | total + rel.distance) AS total_distance </code></pre></div> <h5 id="all-paths" class="position-relative d-flex align-items-center group"> All Paths <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="all-paths" aria-haspopup="dialog" aria-label="Share link: All Paths"> Share link </button> </h5>Enumerate all paths between nodes: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">// Find all paths up to length 5 MATCH path = (start:Node {id: 1})-[*1..5]->(end:Node {id: 100}) RETURN path, LENGTH(path) AS path_length ORDER BY path_length </code></pre></div> <h5 id="a-search" class="position-relative d-flex align-items-center group"> A* Search <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="a-search" aria-haspopup="dialog" aria-label="Share link: A* Search"> Share link </button> </h5>Implement heuristic pathfinding with property-based weighting: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">// Weighted path with heuristic MATCH path = (start:Location)-[r:CONNECTED*]-(goal:Location) WHERE start.name = 'Start' AND goal.name = 'Goal' WITH path, REDUCE(cost = 0, rel IN r | cost + rel.weight) AS total_cost, LENGTH(path) AS hops ORDER BY total_cost + hops * 10 // A* heuristic: cost + estimated remaining LIMIT 1 RETURN path, total_cost </code></pre></div> <h4 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> </h4> <h5 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> </h5>Count incoming and outgoing relationships: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">// Out-degree centrality (influence) MATCH (u:User)-[r:FOLLOWS]->() RETURN u.name, COUNT(r) AS followers ORDER BY followers DESC LIMIT 10 // In-degree centrality (popularity) MATCH (u:User)<-[r:FOLLOWS]-() RETURN u.name, COUNT(r) AS following ORDER BY following DESC LIMIT 10 </code></pre></div> <h5 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> </h5>Identify nodes that frequently lie on shortest paths: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">// Nodes that bridge communities MATCH path = SHORTEST (a:Person)-[:KNOWS*]-(b:Person) WHERE a.id < b.id // Avoid duplicates WITH NODES(path) AS nodes UNWIND nodes AS node WITH node, COUNT(*) AS times_on_shortest_path WHERE times_on_shortest_path > 1 RETURN node.name, times_on_shortest_path ORDER BY times_on_shortest_path DESC LIMIT 10 </code></pre></div> <h5 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> </h5>Iterative algorithm for ranking node importance: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python"># Python implementation using Geode client from geode_client import Client async def pagerank(client, damping=0.85, iterations=20): # Initialize PageRank scores await client.query(""" MATCH (n:Page) SET n.pagerank = 1.0 """) for i in range(iterations): # Update PageRank scores result, _ = await client.query(""" MATCH (source:Page)-[:LINKS]->(target:Page) WITH target, source, COUNT(*) AS out_degree MATCH (source)-[:LINKS]->() WITH target, SUM(source.pagerank / out_degree) AS rank_sum SET target.new_pagerank = $damping * rank_sum + (1 - $damping) RETURN AVG(ABS(target.new_pagerank - target.pagerank)) AS delta """, {"damping": damping}) # Commit new scores await client.query("MATCH (n:Page) SET n.pagerank = n.new_pagerank") if result.rows[0]['delta'] < 0.0001: break return await client.query(""" MATCH (n:Page) RETURN n.url, n.pagerank ORDER BY n.pagerank DESC LIMIT 20 """) </code></pre></div> <h4 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> </h4> <h5 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> </h5>Detect communities by propagating labels: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">// Initialize labels MATCH (n:User) SET n.community = n.id // Propagate (repeat multiple times) MATCH (n:User)-[:KNOWS]-(neighbor:User) WITH n, neighbor.community AS neighbor_label, COUNT(*) AS frequency ORDER BY n, frequency DESC WITH n, COLLECT(neighbor_label)[0] AS most_common SET n.community = most_common </code></pre></div> <h5 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> </h5>Find disconnected subgraphs: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">// Identify weakly connected components MATCH path = (n:Node)-[*]-(m:Node) WITH n, COLLECT(DISTINCT m.id) AS component RETURN MIN(component) AS component_id, COUNT(*) AS size ORDER BY size DESC </code></pre></div> <h5 id="triangle-counting" class="position-relative d-flex align-items-center group"> Triangle Counting <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" aria-haspopup="dialog" aria-label="Share link: Triangle Counting"> Share link </button> </h5>Count triangles for clustering coefficient: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">// Find triangles in social network MATCH (a:User)-[:KNOWS]->(b:User)-[:KNOWS]->(c:User)-[:KNOWS]->(a) WHERE a.id < b.id AND b.id < c.id // Avoid duplicates RETURN COUNT(*) AS triangle_count // Clustering coefficient per node MATCH (u:User)-[:KNOWS]-(neighbor:User) WITH u, COLLECT(DISTINCT neighbor) AS neighbors, COUNT(DISTINCT neighbor) AS degree WHERE degree > 1 UNWIND neighbors AS n1 UNWIND neighbors AS n2 WITH u, n1, n2, degree WHERE n1.id < n2.id MATCH (n1)-[r:KNOWS]-(n2) WITH u, COUNT(r) AS actual_triangles, degree * (degree - 1) / 2 AS possible_triangles RETURN u.name, actual_triangles * 1.0 / possible_triangles AS clustering_coefficient ORDER BY clustering_coefficient DESC </code></pre></div> <h4 id="similarity-algorithms" class="position-relative d-flex align-items-center group"> Similarity 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="similarity-algorithms" aria-haspopup="dialog" aria-label="Share link: Similarity Algorithms"> Share link </button> </h4> <h5 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> </h5>Compute similarity based on common neighbors: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">// Find similar users by common interests MATCH (u1:User {id: 123})-[:LIKES]->(item:Item)<-[:LIKES]-(u2:User) WHERE u1.id <> u2.id WITH u1, u2, COUNT(DISTINCT item) AS common_interests MATCH (u1)-[:LIKES]->(item1:Item) WITH u1, u2, common_interests, COUNT(DISTINCT item1) AS u1_interests MATCH (u2)-[:LIKES]->(item2:Item) WITH u1, u2, common_interests, u1_interests, COUNT(DISTINCT item2) AS u2_interests WITH u1, u2, common_interests * 1.0 / (u1_interests + u2_interests - common_interests) AS jaccard WHERE jaccard > 0.3 RETURN u2.name, jaccard ORDER BY jaccard DESC LIMIT 10 </code></pre></div> <h5 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> </h5>Measure similarity using property vectors: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python"># Python implementation with embeddings async def cosine_similarity(client, user_id, limit=10): result, _ = await client.query(""" MATCH (u1:User {id: $user_id}) MATCH (u2:User) WHERE u2.id <> $user_id WITH u1, u2, REDUCE(dot = 0.0, i IN RANGE(0, SIZE(u1.embedding) - 1) | dot + u1.embedding[i] * u2.embedding[i]) AS dot_product, SQRT(REDUCE(norm1 = 0.0, val IN u1.embedding | norm1 + val * val)) AS norm1, SQRT(REDUCE(norm2 = 0.0, val IN u2.embedding | norm2 + val * val)) AS norm2 WITH u2, dot_product / (norm1 * norm2) AS similarity WHERE similarity > 0.5 RETURN u2.name, similarity ORDER BY similarity DESC LIMIT $limit """, {"user_id": user_id, "limit": limit}) return result </code></pre></div> <h3 id="advanced-algorithm-patterns" class="position-relative d-flex align-items-center group"> Advanced Algorithm Patterns <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-algorithm-patterns" aria-haspopup="dialog" aria-label="Share link: Advanced Algorithm Patterns"> Share link </button> </h3> <h4 id="iterative-algorithms" class="position-relative d-flex align-items-center group"> Iterative 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="iterative-algorithms" aria-haspopup="dialog" aria-label="Share link: Iterative Algorithms"> Share link </button> </h4>Many graph algorithms require multiple passes: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-go" data-lang="go">// Go implementation: iterative belief propagation func beliefPropagation(db *sql.DB, iterations int) error { for i := 0; i < iterations; i++ { _, err := db.Exec(` MATCH (n:Node)-[r:EDGE]-(m:Node) WITH n, AVG(m.belief) AS avg_belief SET n.new_belief = 0.5 * n.prior + 0.5 * avg_belief `) if err != nil { return err } _, err = db.Exec(`MATCH (n:Node) SET n.belief = n.new_belief`) if err != nil { return err } } return nil } </code></pre></div> <h4 id="recursive-algorithms" class="position-relative d-flex align-items-center group"> Recursive 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="recursive-algorithms" aria-haspopup="dialog" aria-label="Share link: Recursive Algorithms"> Share link </button> </h4>Depth-first search and traversals: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">// Recursive category hierarchy traversal MATCH path = (root:Category {name: 'Electronics'})-[:SUBCATEGORY*]->(leaf:Category) WHERE NOT EXISTS { MATCH (leaf)-[:SUBCATEGORY]->() } RETURN leaf.name, LENGTH(path) AS depth ORDER BY depth DESC </code></pre></div> <h4 id="parallel-algorithm-execution" class="position-relative d-flex align-items-center group"> Parallel Algorithm Execution <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-algorithm-execution" aria-haspopup="dialog" aria-label="Share link: Parallel Algorithm Execution"> Share link </button> </h4>Execute independent computations in parallel: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-rust" data-lang="rust">// Rust: parallel centrality computation use tokio::task::JoinSet; async fn parallel_centrality(client: &GeodeClient, node_ids: Vec<i64>) -> Result<Vec<f64>> { let mut tasks = JoinSet::new(); for node_id in node_ids { let client = client.clone(); tasks.spawn(async move { let result = client.query(&format!( "MATCH (n {{id: {}}})-[r]->() RETURN COUNT(r) AS degree", node_id )).await?; Ok::<_, Error>(result[0]["degree"].as_f64().unwrap_or(0.0)) }); } let mut centralities = Vec::new(); while let Some(result) = tasks.join_next().await { centralities.push(result??); } Ok(centralities) } </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="algorithm-complexity" class="position-relative d-flex align-items-center group"> Algorithm Complexity <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" aria-haspopup="dialog" aria-label="Share link: Algorithm Complexity"> Share link </button> </h4>Be aware of computational complexity: <ul> <li>Shortest Path (unweighted): O(V + E) with BFS</li> <li>Shortest Path (weighted): O(E + V log V) with Dijkstra</li> <li>PageRank: O(iterations × E)</li> <li>Triangle Counting: O(E^1.5) worst case</li> <li>Label Propagation: O(iterations × E)</li> </ul> <h4 id="optimization-techniques" class="position-relative d-flex align-items-center group"> Optimization Techniques <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="optimization-techniques" aria-haspopup="dialog" aria-label="Share link: Optimization Techniques"> Share link </button> </h4><ol> <li>Limit Traversal Depth: Use path length limits to avoid expensive deep traversals</li> <li>Filter Early: Apply WHERE clauses before expensive operations</li> <li>Use Indexes: Index properties used in algorithm filters</li> <li>Batch Processing: Process large graphs in chunks</li> <li>Materialize Results: Store computed metrics as properties for reuse</li> </ol> <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">// Optimize by limiting depth and filtering early MATCH path = (start:User {id: $id})-[:KNOWS*1..4]-(end:User) WHERE end.active = true // Filter early WITH path, LENGTH(path) AS depth WHERE depth <= 3 // Limit depth RETURN end.name, depth ORDER BY depth LIMIT 100 </code></pre></div> <h3 id="algorithm-libraries" class="position-relative d-flex align-items-center group"> Algorithm Libraries <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-libraries" aria-haspopup="dialog" aria-label="Share link: Algorithm Libraries"> Share link </button> </h3> <h4 id="custom-algorithm-implementation" class="position-relative d-flex align-items-center group"> Custom Algorithm 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="custom-algorithm-implementation" aria-haspopup="dialog" aria-label="Share link: Custom Algorithm Implementation"> Share link </button> </h4>Extend Geode with custom algorithms: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python">class GraphAlgorithms: def __init__(self, client): self.client = client async def detect_cycles(self, start_node_id): """Detect cycles using depth-first search""" visited = set() stack = set() cycles = [] async def dfs(node_id, path): if node_id in stack: cycles.append(path + [node_id]) return if node_id in visited: return visited.add(node_id) stack.add(node_id) result = await self.client.query(""" MATCH (n {id: $id})-[:EDGE]->(m) RETURN m.id AS next_id """, {"id": node_id}) for row in result.rows: await dfs(row['next_id'], path + [node_id]) stack.remove(node_id) await dfs(start_node_id, []) return cycles </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><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">// Identify influencers MATCH (u:User) OPTIONAL MATCH (u)<-[:FOLLOWS]-(follower:User) WITH u, COUNT(follower) AS followers OPTIONAL MATCH (u)-[:POSTED]->(p:Post)<-[:LIKED]-(liker:User) WITH u, followers, COUNT(DISTINCT liker) AS total_likes RETURN u.name, followers, total_likes, (followers + total_likes * 0.5) AS influence_score ORDER BY influence_score DESC LIMIT 20 </code></pre></div> <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">// Detect suspicious transaction rings MATCH path = (a:Account)-[:TRANSFERRED*3..6]->(a) WHERE ALL(r IN relationships(path) WHERE r.amount > 10000) WITH path, REDUCE(total = 0, r IN relationships(path) | total + r.amount) AS ring_total WHERE ring_total > 100000 RETURN path, ring_total ORDER BY ring_total DESC </code></pre></div> <h4 id="recommendation-systems" class="position-relative d-flex align-items-center group"> Recommendation Systems <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-systems" aria-haspopup="dialog" aria-label="Share link: Recommendation Systems"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">// Collaborative filtering recommendations MATCH (u:User {id: $user_id})-[:PURCHASED]->(p:Product)<-[:PURCHASED]-(similar:User) WHERE similar.id <> $user_id WITH similar, COUNT(p) AS common_purchases ORDER BY common_purchases DESC LIMIT 10 MATCH (similar)-[:PURCHASED]->(recommendation:Product) WHERE NOT EXISTS { MATCH (u:User {id: $user_id})-[:PURCHASED]->(recommendation) } WITH recommendation, COUNT(similar) AS recommender_count RETURN recommendation.name, recommender_count ORDER BY recommender_count DESC LIMIT 5 </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><ol> <li>Understand Complexity: Profile algorithms with realistic data before production deployment</li> <li>Set Limits: Always bound path lengths and iteration counts</li> <li>Use Sampling: For large graphs, sample subgraphs for approximate results</li> <li>Cache Results: Materialize frequently computed metrics as node properties</li> <li>Monitor Performance: Track algorithm execution time and resource usage</li> <li>Parallelize When Possible: Leverage concurrent execution for independent computations</li> <li>Validate Results: Test algorithms on known datasets with expected outcomes</li> </ol> <h3 id="common-pitfalls" class="position-relative d-flex align-items-center group"> Common Pitfalls <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="common-pitfalls" aria-haspopup="dialog" aria-label="Share link: Common Pitfalls"> Share link </button> </h3><ol> <li>Unbounded Traversals: Not limiting path depth can cause exponential explosion</li> <li>Dense Node Performance: Algorithms on hub nodes (millions of relationships) can be slow</li> <li>Ignoring Direction: Forgetting to consider relationship direction in directed graphs</li> <li>Memory Constraints: Large intermediate results can exceed available memory</li> <li>Algorithm Mismatch: Using wrong algorithm for the problem (e.g., shortest path when all paths needed)</li> </ol> <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/graph-algorithms/" >Graph Algorithms</a> - Graph algorithm implementations</li> <li><a href="/tags/query-optimization/" >Query Optimization</a> - Tune GQL queries for algorithm performance</li> <li><a href="/tags/indexing/" >Indexing</a> - Create indexes to accelerate algorithm execution</li> <li><a href="/tags/performance/" >Performance</a> - Optimize database configuration for graph 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><a href="/docs/tutorials/graph-algorithms-tutorial/" >Graph Algorithms Tutorial</a> - Complete graph algorithms tutorial</li> <li><a href="/docs/gql-reference/" >GQL Reference</a> - Complete language documentation</li> <li><a href="/docs/client-libraries/" >Client Libraries</a> - Implement algorithms in Python, Go, Rust, Zig</li> </ul> <h3 id="advanced-pathfinding-algorithms" class="position-relative d-flex align-items-center group"> Advanced Pathfinding 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="advanced-pathfinding-algorithms" aria-haspopup="dialog" aria-label="Share link: Advanced Pathfinding Algorithms"> Share link </button> </h3> <h4 id="k-shortest-paths" class="position-relative d-flex align-items-center group"> K-Shortest Paths <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-shortest-paths" aria-haspopup="dialog" aria-label="Share link: K-Shortest Paths"> Share link </button> </h4>Find multiple alternative paths: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python">async def k_shortest_paths(client, start_id, end_id, k=5): """Find k shortest paths between nodes using Yen's algorithm""" paths = [] # Find first shortest path result, _ = await client.query(""" MATCH path = shortestPath((start {id: $start})-[*]-(end {id: $end})) RETURN path """, {"start": start_id, "end": end_id}) if not result: return paths paths.append(result.rows[0]['path']) # Find k-1 additional paths for _ in range(k - 1): candidates = [] # For each spur node in previous path for i in range(len(paths[-1].nodes) - 1): # Remove edges from previous paths # Find detour through remaining graph # Add to candidates pass # Implementation details if not candidates: break # Add best candidate to paths paths.append(min(candidates, key=lambda p: path_cost(p))) return paths </code></pre></div> <h4 id="bidirectional-search" class="position-relative d-flex align-items-center group"> Bidirectional Search <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="bidirectional-search" aria-haspopup="dialog" aria-label="Share link: Bidirectional Search"> Share link </button> </h4>Faster pathfinding for long paths: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Search from both ends simultaneously MATCH forward = (start {id: $start})-[*1..10]->(mid) MATCH backward = (end {id: $end})-[*1..10]->(mid) WHERE start.id <> end.id RETURN forward + backward AS complete_path, length(forward) + length(backward) AS total_length ORDER BY total_length LIMIT 1 </code></pre></div> <h4 id="constrained-pathfinding" class="position-relative d-flex align-items-center group"> Constrained Pathfinding <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="constrained-pathfinding" aria-haspopup="dialog" aria-label="Share link: Constrained Pathfinding"> Share link </button> </h4>Paths that satisfy conditions: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Path through specific node types MATCH path = (start:Airport {code: 'SFO'})-[:FLIGHT*]-(end:Airport {code: 'JFK'}) WHERE ALL(node IN nodes(path) WHERE node:Airport OR node:Hub) AND NONE(rel IN relationships(path) WHERE rel.canceled = true) RETURN path, REDUCE(cost = 0, rel IN relationships(path) | cost + rel.price) AS total_cost ORDER BY total_cost LIMIT 1 -- Time-constrained paths MATCH path = (start:Station)-[:ROUTE*]->(end:Station) WHERE start.name = 'Downtown' AND end.name = 'Airport' AND REDUCE(time = 0, rel IN relationships(path) | time + rel.travel_minutes) <= 60 RETURN path ORDER BY length(path) LIMIT 1 </code></pre></div> <h3 id="production-centrality-analysis" class="position-relative d-flex align-items-center group"> Production Centrality 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="production-centrality-analysis" aria-haspopup="dialog" aria-label="Share link: Production Centrality Analysis"> Share link </button> </h3> <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>Measure influence based on connection quality: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python">import numpy as np async def eigenvector_centrality(client, iterations=100, tolerance=1e-6): """Compute eigenvector centrality using power iteration""" # Get adjacency matrix nodes, _ = await client.query("MATCH (n) RETURN n.id AS id ORDER BY id") node_ids = [row['id'] for row in nodes] n = len(node_ids) id_to_index = {node_id: i for i, node_id in enumerate(node_ids)} # Build adjacency matrix adj = np.zeros((n, n)) edges, _ = await client.query(""" MATCH (a)-[:CONNECTED]->(b) RETURN a.id AS source, b.id AS target """) for edge in edges: i = id_to_index[edge['source']] j = id_to_index[edge['target']] adj[i][j] = 1 # Power iteration x = np.ones(n) / n for _ in range(iterations): x_new = adj @ x x_new = x_new / np.linalg.norm(x_new) if np.linalg.norm(x_new - x) < tolerance: break x = x_new # Store results back for node_id, score in zip(node_ids, x): await client.execute(""" MATCH (n {id: $id}) SET n.eigenvector_centrality = $score """, {"id": node_id, "score": float(score)}) return dict(zip(node_ids, x)) </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>Measure average distance to all other nodes: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Average shortest path length from each node MATCH (source:Person) MATCH (target:Person) WHERE source.id <> target.id WITH source, REDUCE(total = 0, path IN COLLECT(shortestPath((source)-[*]-(target))) | total + length(path)) AS sum_distances, COUNT(target) AS target_count WITH source, (target_count - 1) / sum_distances AS closeness RETURN source.name, closeness ORDER BY closeness DESC LIMIT 10 </code></pre></div> <h4 id="harmonic-centrality" class="position-relative d-flex align-items-center group"> Harmonic 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="harmonic-centrality" aria-haspopup="dialog" aria-label="Share link: Harmonic Centrality"> Share link </button> </h4>Robust variant of closeness centrality: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Sum of reciprocal distances MATCH (source:Person) OPTIONAL MATCH path = shortestPath((source)-[*]-(target:Person)) WHERE source.id <> target.id WITH source, SUM(1.0 / length(path)) AS harmonic_centrality RETURN source.name, harmonic_centrality ORDER BY harmonic_centrality DESC </code></pre></div> <h3 id="community-detection-algorithms" class="position-relative d-flex align-items-center group"> Community Detection 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="community-detection-algorithms" aria-haspopup="dialog" aria-label="Share link: Community Detection Algorithms"> Share link </button> </h3> <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>Hierarchical community detection: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python">async def louvain_algorithm(client, resolution=1.0): """Louvain community detection algorithm""" # Phase 1: Assign each node to own community await client.execute(""" MATCH (n) SET n.community = n.id """) improved = True iteration = 0 while improved and iteration < 100: improved = False iteration += 1 # For each node, try moving to neighbor's community nodes, _ = await client.query("MATCH (n) RETURN n.id AS id") for node in nodes: node_id = node['id'] # Get current modularity current_modularity = await compute_modularity(client) # Try each neighbor's community neighbors, _ = await client.query(""" MATCH (n {id: $id})-[:CONNECTED]-(neighbor) RETURN DISTINCT neighbor.community AS community """, {"id": node_id}) best_community = None best_modularity = current_modularity for neighbor in neighbors: # Try moving to this community test_modularity = await test_community_move( client, node_id, neighbor['community'] ) if test_modularity > best_modularity: best_modularity = test_modularity best_community = neighbor['community'] # Move to best community if improvement found if best_community is not None: await client.execute(""" MATCH (n {id: $id}) SET n.community = $community """, {"id": node_id, "community": best_community}) improved = True # Phase 2: Build super-graph of communities if not improved: await build_community_graph(client) return await get_community_assignments(client) </code></pre></div> <h4 id="girvan-newman-algorithm" class="position-relative d-flex align-items-center group"> Girvan-Newman 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="girvan-newman-algorithm" aria-haspopup="dialog" aria-label="Share link: Girvan-Newman Algorithm"> Share link </button> </h4>Edge betweenness-based community detection: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Iteratively remove edges with highest betweenness MATCH path = allShortestPaths((a:Node)-[*]-(b:Node)) WHERE a.id < b.id UNWIND relationships(path) AS edge WITH edge, COUNT(*) AS betweenness ORDER BY betweenness DESC LIMIT 1 DELETE edge -- Repeat until desired number of communities reached </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>Find maximal strongly connected subgraphs: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python">async def tarjan_scc(client): """Tarjan's algorithm for strongly connected components""" # Get all nodes nodes, _ = await client.query("MATCH (n) RETURN n.id AS id") node_list = [n['id'] for n in nodes] index = 0 stack = [] indices = {} lowlinks = {} on_stack = set() sccs = [] async def strongconnect(node_id): nonlocal index indices[node_id] = index lowlinks[node_id] = index index += 1 stack.append(node_id) on_stack.add(node_id) # Get successors successors, _ = await client.query(""" MATCH (n {id: $id})-[:EDGE]->(successor) RETURN successor.id AS id """, {"id": node_id}) for succ in successors: succ_id = succ['id'] if succ_id not in indices: await strongconnect(succ_id) lowlinks[node_id] = min(lowlinks[node_id], lowlinks[succ_id]) elif succ_id in on_stack: lowlinks[node_id] = min(lowlinks[node_id], indices[succ_id]) # Root of SCC if lowlinks[node_id] == indices[node_id]: scc = [] while True: w = stack.pop() on_stack.remove(w) scc.append(w) if w == node_id: break sccs.append(scc) for node_id in node_list: if node_id not in indices: await strongconnect(node_id) return sccs </code></pre></div> <h3 id="advanced-similarity-algorithms" class="position-relative d-flex align-items-center group"> Advanced Similarity 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="advanced-similarity-algorithms" aria-haspopup="dialog" aria-label="Share link: Advanced Similarity Algorithms"> Share link </button> </h3> <h4 id="simrank" class="position-relative d-flex align-items-center group"> SimRank <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="simrank" aria-haspopup="dialog" aria-label="Share link: SimRank"> Share link </button> </h4>Iterative similarity based on neighborhood: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python">async def simrank(client, decay=0.8, max_iterations=10): """SimRank similarity algorithm""" nodes, _ = await client.query("MATCH (n) RETURN n.id AS id") node_list = [n['id'] for n in nodes] n = len(node_list) # Initialize similarity matrix sim = {(a, b): 1.0 if a == b else 0.0 for a in node_list for b in node_list} for iteration in range(max_iterations): sim_new = {} for a in node_list: for b in node_list: if a == b: sim_new[(a, b)] = 1.0 continue # Get in-neighbors a_in = await get_in_neighbors(client, a) b_in = await get_in_neighbors(client, b) if not a_in or not b_in: sim_new[(a, b)] = 0.0 continue # Compute similarity total = sum(sim[(i, j)] for i in a_in for j in b_in) sim_new[(a, b)] = (decay / (len(a_in) * len(b_in))) * total sim = sim_new # Store similarities for (a, b), score in sim.items(): if a < b and score > 0.1: # Store only significant similarities await client.execute(""" MATCH (a {id: $a}), (b {id: $b}) MERGE (a)-[s:SIMILAR_TO]->(b) SET s.simrank_score = $score """, {"a": a, "b": b, "score": score}) return sim </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>Link prediction scoring: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Predict future links MATCH (a:User {id: $user_id}) MATCH (a)-[:KNOWS]-(mutual)-[:KNOWS]-(b:User) WHERE a.id <> b.id AND NOT EXISTS { MATCH (a)-[:KNOWS]-(b) } WITH b, COUNT(DISTINCT mutual) AS mutual_friends, SUM(1.0 / log(COUNT{ MATCH (mutual)-[:KNOWS]-() })) AS aa_score RETURN b.name, mutual_friends, aa_score ORDER BY aa_score DESC LIMIT 10 </code></pre></div> <h3 id="machine-learning-integration" class="position-relative d-flex align-items-center group"> Machine Learning Integration <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="machine-learning-integration" aria-haspopup="dialog" aria-label="Share link: Machine Learning Integration"> Share link </button> </h3> <h4 id="graph-embedding" class="position-relative d-flex align-items-center group"> Graph Embedding <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-embedding" aria-haspopup="dialog" aria-label="Share link: Graph Embedding"> Share link </button> </h4>Convert graph structure to vectors: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python">from node2vec import Node2Vec import networkx as nx async def generate_embeddings(client, dimensions=128): """Generate node embeddings using node2vec""" # Export graph to NetworkX G = nx.Graph() nodes, _ = await client.query("MATCH (n) RETURN n.id AS id") for node in nodes: G.add_node(node['id']) edges, _ = await client.query(""" MATCH (a)-[:CONNECTED]-(b) RETURN a.id AS source, b.id AS target """) for edge in edges: G.add_edge(edge['source'], edge['target']) # Generate embeddings node2vec = Node2Vec(G, dimensions=dimensions, walk_length=30, num_walks=200) model = node2vec.fit(window=10, min_count=1, batch_words=4) # Store embeddings back for node_id in G.nodes(): embedding = model.wv[node_id].tolist() await client.execute(""" MATCH (n {id: $id}) SET n.embedding = $embedding """, {"id": node_id, "embedding": embedding}) return model </code></pre></div> <h4 id="graph-neural-networks" class="position-relative d-flex align-items-center group"> Graph Neural Networks <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-neural-networks" aria-haspopup="dialog" aria-label="Share link: Graph Neural Networks"> Share link </button> </h4>Classification using GNN: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python">import torch import torch_geometric async def train_gnn_classifier(client, num_classes, hidden_channels=64): """Train GNN for node classification""" # Load graph data data = await load_graph_data(client) class GCN(torch.nn.Module): def __init__(self): super().__init__() self.conv1 = GCNConv(data.num_features, hidden_channels) self.conv2 = GCNConv(hidden_channels, num_classes) def forward(self, x, edge_index): x = self.conv1(x, edge_index) x = x.relu() x = F.dropout(x, p=0.5, training=self.training) x = self.conv2(x, edge_index) return x model = GCN() optimizer = torch.optim.Adam(model.parameters(), lr=0.01) criterion = torch.nn.CrossEntropyLoss() # Training loop model.train() for epoch in range(200): optimizer.zero_grad() out = model(data.x, data.edge_index) loss = criterion(out[data.train_mask], data.y[data.train_mask]) loss.backward() optimizer.step() # Store predictions model.eval() pred = model(data.x, data.edge_index).argmax(dim=1) for node_id, prediction in zip(data.node_ids, pred): await client.execute(""" MATCH (n {id: $id}) SET n.predicted_class = $class """, {"id": node_id, "class": int(prediction)}) return model </code></pre></div> <h3 id="algorithm-performance-optimization" class="position-relative d-flex align-items-center group"> Algorithm 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="algorithm-performance-optimization" aria-haspopup="dialog" aria-label="Share link: Algorithm Performance Optimization"> Share link </button> </h3> <h4 id="parallel-execution" class="position-relative d-flex align-items-center group"> Parallel Execution <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-execution" aria-haspopup="dialog" aria-label="Share link: Parallel Execution"> Share link </button> </h4>Distribute computation across cores: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python">import asyncio from concurrent.futures import ThreadPoolExecutor async def parallel_centrality_computation(client, node_ids): """Compute centrality for nodes in parallel""" async def compute_node_centrality(node_id): result, _ = await client.query(""" MATCH (n {id: $id})-[r]-() RETURN COUNT(r) AS degree """, {"id": node_id}) return node_id, result.rows[0]['degree'] # Create tasks for all nodes tasks = [compute_node_centrality(nid) for nid in node_ids] # Execute in parallel (limited concurrency) semaphore = asyncio.Semaphore(50) async def bounded_task(task): async with semaphore: return await task results = await asyncio.gather(*[bounded_task(t) for t in tasks]) return dict(results) </code></pre></div> <h4 id="approximate-algorithms" class="position-relative d-flex align-items-center group"> Approximate 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="approximate-algorithms" aria-haspopup="dialog" aria-label="Share link: Approximate Algorithms"> Share link </button> </h4>Trade accuracy for speed: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Approximate PageRank with sampling MATCH (n:Node) WITH n, rand() AS random WHERE random < 0.1 // Sample 10% of nodes MATCH (n)-[:CONNECTED*1..5]-(connected) WITH n, COUNT(DISTINCT connected) AS approx_reach RETURN n.id, approx_reach ORDER BY approx_reach DESC LIMIT 100 </code></pre></div> <h4 id="incremental-computation" class="position-relative d-flex align-items-center group"> Incremental Computation <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="incremental-computation" aria-haspopup="dialog" aria-label="Share link: Incremental Computation"> Share link </button> </h4>Update algorithms without full recomputation: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python">async def incremental_pagerank(client, new_edge): """Update PageRank incrementally after edge addition""" # Only recompute affected nodes affected, _ = await client.query(""" MATCH path = (source {id: $source})-[:CONNECTED*0..2]-(affected) RETURN DISTINCT affected.id AS id """, {"source": new_edge['source']}) # Recompute only affected subgraph for node in affected: await update_pagerank_for_node(client, node['id']) </code></pre></div> <h3 id="monitoring-and-debugging-algorithms" class="position-relative d-flex align-items-center group"> Monitoring and Debugging 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="monitoring-and-debugging-algorithms" aria-haspopup="dialog" aria-label="Share link: Monitoring and Debugging Algorithms"> Share link </button> </h3> <h4 id="algorithm-profiling" class="position-relative d-flex align-items-center group"> Algorithm Profiling <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-profiling" aria-haspopup="dialog" aria-label="Share link: Algorithm Profiling"> Share link </button> </h4>Track execution performance: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python">import time async def profile_algorithm(algorithm_func, *args, **kwargs): """Profile algorithm execution""" start_time = time.time() start_memory = get_memory_usage() result = await algorithm_func(*args, **kwargs) end_time = time.time() end_memory = get_memory_usage() print(f"Execution time: {end_time - start_time:.2f}s") print(f"Memory used: {end_memory - start_memory:.2f}MB") print(f"Results: {len(result.rows)} items") return result </code></pre></div> <h4 id="visualization" class="position-relative d-flex align-items-center group"> Visualization <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="visualization" aria-haspopup="dialog" aria-label="Share link: Visualization"> Share link </button> </h4>Visualize algorithm results: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python">import matplotlib.pyplot as plt import networkx as nx async def visualize_communities(client): """Visualize community detection results""" G = nx.Graph() # Load graph with community labels edges, _ = await client.query(""" MATCH (a)-[:CONNECTED]-(b) RETURN a.id AS source, b.id AS target, a.community AS comm_a, b.community AS comm_b """) for edge in edges: G.add_edge(edge['source'], edge['target']) # Color by community communities, _ = await client.query(""" MATCH (n) RETURN n.id AS id, n.community AS community """) community_map = {n['id']: n['community'] for n in communities} colors = [community_map[node] for node in G.nodes()] # Draw pos = nx.spring_layout(G) nx.draw(G, pos, node_color=colors, with_labels=True, cmap=plt.cm.rainbow) plt.savefig('communities.png') </code></pre></div>Graph algorithms unlock the analytical power of connected data. Start with simple pathfinding and centrality computations, then progress to advanced community detection and machine learning integration as your graph expertise grows. Geode’s GQL-native implementation provides excellent performance for production workloads while maintaining code clarity and maintainability.

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