Tag: Graph Algorithms & Analytics

<h2 id="graph-algorithms--analytics-in-geode" class="position-relative d-flex align-items-center group"> Graph Algorithms &amp; Analytics 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="graph-algorithms--analytics-in-geode" aria-haspopup="dialog" aria-label="Share link: Graph Algorithms &amp; Analytics 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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From finding shortest paths and detecting communities to ranking influential nodes and identifying anomalies, graph algorithms are essential tools for modern data science and analytics. Geode provides optimized implementations of classic and advanced graph algorithms, all accessible through GQL queries. These algorithms leverage Geode’s native graph storage and parallel processing capabilities to deliver high performance even on massive graphs with billions of nodes and relationships. This comprehensive guide explores essential graph algorithms, their mathematical foundations, complexity analysis, implementation patterns, and optimization strategies for production deployments. <h3 id="theoretical-foundations" class="position-relative d-flex align-items-center group"> Theoretical Foundations <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="theoretical-foundations" aria-haspopup="dialog" aria-label="Share link: Theoretical Foundations"> Share link </button> </h3> <h4 id="graph-complexity-classes" class="position-relative d-flex align-items-center group"> Graph Complexity Classes <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-complexity-classes" aria-haspopup="dialog" aria-label="Share link: Graph Complexity Classes"> Share link </button> </h4>Understanding algorithmic complexity is crucial for choosing the right algorithm for your data size: Polynomial Time (P): <ul> <li>Single-source shortest path: O(V + E) with BFS, O((V + E) log V) with Dijkstra</li> <li>Minimum spanning tree: O(E log V) with Kruskal’s, O(E + V log V) with Prim’s</li> <li>PageRank (fixed iterations): O(k × E) where k is iteration count</li> <li>Strongly connected components: O(V + E) with Tarjan’s algorithm</li> </ul> NP-Complete (Intractable): <ul> <li>Hamiltonian path/cycle: O(2^V × V^2)</li> <li>Graph coloring: O(k^V) where k is number of colors</li> <li>Traveling salesman problem (TSP): O(V! / 2)</li> <li>Maximum clique: O(3^(V/3))</li> </ul> Approximation Algorithms (when exact solutions are impractical): <ul> <li>Community detection: Modularity optimization O(V × E)</li> <li>Betweenness centrality sampling: O(k × V × E) where k « V</li> <li>Graph partitioning: Spectral methods O(V^3)</li> </ul> <h4 id="graph-properties-and-invariants" class="position-relative d-flex align-items-center group"> Graph Properties and Invariants <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-properties-and-invariants" aria-haspopup="dialog" aria-label="Share link: Graph Properties and Invariants"> Share link </button> </h4>Degree Distribution: Characterizes network topology <ul> <li>Regular graphs: All nodes have same degree</li> <li>Scale-free networks: Power-law degree distribution P(k) ~ k^(-γ)</li> <li>Small-world networks: High clustering, short average path length</li> </ul> Clustering Coefficient: Measures local density <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-fallback" data-lang="fallback">C(v) = 2 × |{(u,w) : u,w ∈ N(v) ∧ (u,w) ∈ E}| / (deg(v) × (deg(v) - 1)) </code></pre></div>Graph Diameter: Maximum shortest path between any two nodes Graph Density: Ratio of actual edges to possible edges = E / (V × (V-1) / 2) <h3 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> </h3>Shortest Path (Dijkstra): <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Find shortest path between two nodes MATCH path = shortestPath( (start:Location {name: 'New York'})-[:ROUTE*]-(end:Location {name: 'Los Angeles'}) ) RETURN path, length(path) as hops; -- Weighted shortest path MATCH path = shortestPath( (start:Location {name: 'New York'})-[r:ROUTE*]-(end:Location {name: 'Los Angeles'}) ) RETURN path, reduce(dist = 0, rel in relationships(path) | dist + rel.distance) as total_distance; </code></pre></div>All Shortest Paths: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Find all shortest paths (when multiple exist) MATCH paths = allShortestPaths( (a:Person {id: 123})-[:KNOWS*]-(b:Person {id: 456}) ) RETURN paths, length(paths) as path_length; </code></pre></div>K-Shortest Paths: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Find top K shortest paths MATCH path = (start:City {name: 'Boston'})-[:CONNECTED*1..10]-(end:City {name: 'Seattle'}) WITH path, reduce(cost = 0, r in relationships(path) | cost + r.weight) as total_cost ORDER BY total_cost LIMIT 5 RETURN path, total_cost; </code></pre></div> <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>Degree Centrality: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Calculate in-degree (followers) MATCH (u:User) OPTIONAL MATCH (u)<-[:FOLLOWS]-(follower:User) RETURN u.name, count(follower) as in_degree ORDER BY in_degree DESC LIMIT 10; -- Out-degree (following) MATCH (u:User) OPTIONAL MATCH (u)-[:FOLLOWS]->(following:User) RETURN u.name, count(following) as out_degree ORDER BY out_degree DESC; -- Total degree MATCH (u:User) OPTIONAL MATCH (u)-[:KNOWS]-(connected:User) RETURN u.name, count(DISTINCT connected) as degree ORDER BY degree DESC; </code></pre></div>Betweenness Centrality (nodes on shortest paths): <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Simplified betweenness calculation MATCH (n:Person) MATCH path = shortestPath((a:Person)-[:KNOWS*]-(b:Person)) WHERE n IN nodes(path) AND a <> n AND b <> n WITH n, count(path) as paths_through RETURN n.name, paths_through ORDER BY paths_through DESC LIMIT 10; </code></pre></div>Closeness Centrality (average distance to others): <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Measure how close a node is to all others MATCH (u:User {id: 123}) MATCH path = shortestPath((u)-[:KNOWS*]-(other:User)) WHERE other <> u WITH u, avg(length(path)) as avg_distance RETURN u.name, 1.0 / avg_distance as closeness_centrality; </code></pre></div> <h3 id="pagerank-and-influence" class="position-relative d-flex align-items-center group"> PageRank and Influence <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-and-influence" aria-haspopup="dialog" aria-label="Share link: PageRank and Influence"> Share link </button> </h3>Basic PageRank Implementation: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Simplified PageRank-style scoring MATCH (u:User)<-[:FOLLOWS]-(follower:User) WITH u, count(follower) as direct_followers MATCH (follower)<-[:FOLLOWS]-(indirect:User) RETURN u.name, direct_followers, count(DISTINCT indirect) as indirect_reach, direct_followers * 1.0 + count(DISTINCT indirect) * 0.15 as influence_score ORDER BY influence_score DESC; </code></pre></div>Weighted Influence: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Account for follower quality MATCH (u:User)<-[f:FOLLOWS]-(follower:User) OPTIONAL MATCH (follower)<-[:FOLLOWS]-(follower_of_follower:User) WITH u, follower, count(follower_of_follower) as follower_influence RETURN u.name, sum(follower_influence) as weighted_influence ORDER BY weighted_influence DESC; </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>Connected Components: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Find connected components MATCH (start:User {id: 123})-[:KNOWS*]-(connected:User) RETURN collect(DISTINCT connected.id) as community_members, count(DISTINCT connected) as community_size; </code></pre></div>Triangle Counting (clustered communities): <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Count triangles (A knows B, B knows C, C knows A) MATCH (a:User)-[:KNOWS]->(b:User)-[:KNOWS]->(c:User)-[:KNOWS]->(a) RETURN count(*) / 3 as triangle_count; -- Local clustering coefficient MATCH (u:User {id: 123})-[:KNOWS]-(neighbor:User) WITH u, collect(DISTINCT neighbor) as neighbors, count(DISTINCT neighbor) as degree UNWIND neighbors as n1 UNWIND neighbors as n2 MATCH (n1)-[r:KNOWS]-(n2) WHERE n1 <> n2 WITH u, degree, count(DISTINCT r) as connected_pairs RETURN u.name, degree, connected_pairs * 2.0 / (degree * (degree - 1)) as clustering_coefficient; </code></pre></div>Label Propagation (community discovery): <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Simplified label propagation MATCH (u:User)-[:KNOWS]-(neighbor:User) WITH u, neighbor.community_id as neighbor_community, count(*) as freq ORDER BY freq DESC LIMIT 1 SET u.community_id = neighbor_community RETURN u.name, u.community_id; </code></pre></div> <h3 id="similarity-and-recommendations" class="position-relative d-flex align-items-center group"> Similarity and Recommendations <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-and-recommendations" aria-haspopup="dialog" aria-label="Share link: Similarity and Recommendations"> Share link </button> </h3>Jaccard Similarity (common connections): <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Find similar users by shared connections MATCH (u1:User {id: 123})-[:FOLLOWS]->(common:User)<-[:FOLLOWS]-(u2:User) WHERE u1 <> u2 WITH u1, u2, count(DISTINCT common) as common_count MATCH (u1)-[:FOLLOWS]->(u1_following:User) MATCH (u2)-[:FOLLOWS]->(u2_following:User) WITH u1, u2, common_count, count(DISTINCT u1_following) as u1_total, count(DISTINCT u2_following) as u2_total RETURN u2.name, common_count * 1.0 / (u1_total + u2_total - common_count) as jaccard_similarity ORDER BY jaccard_similarity DESC LIMIT 10; </code></pre></div>Collaborative Filtering: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Recommend products based on similar users' purchases MATCH (u:User {id: 123})-[:PURCHASED]->(p:Product)<-[:PURCHASED]-(similar:User) WHERE similar <> u WITH similar, count(DISTINCT p) as common_purchases ORDER BY common_purchases DESC LIMIT 50 MATCH (similar)-[:PURCHASED]->(recommendation:Product) WHERE NOT EXISTS {(u)-[:PURCHASED]->(recommendation)} RETURN recommendation.name, count(*) as recommendation_score ORDER BY recommendation_score DESC LIMIT 10; </code></pre></div>Cosine Similarity (vector-based): <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Compare users by behavior vectors MATCH (u1:User {id: 123})-[r1:RATED]->(item:Product)<-[r2:RATED]-(u2:User) WHERE u1 <> u2 WITH u1, u2, sum(r1.rating * r2.rating) as dot_product, sqrt(sum(r1.rating * r1.rating)) as u1_magnitude, sqrt(sum(r2.rating * r2.rating)) as u2_magnitude RETURN u2.name, dot_product / (u1_magnitude * u2_magnitude) as cosine_similarity ORDER BY cosine_similarity DESC; </code></pre></div> <h3 id="graph-traversal-algorithms" class="position-relative d-flex align-items-center group"> Graph Traversal 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="graph-traversal-algorithms" aria-haspopup="dialog" aria-label="Share link: Graph Traversal Algorithms"> Share link </button> </h3>Breadth-First Search (BFS): <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Explore network level by level MATCH path = (start:User {id: 123})-[:KNOWS*1..4]-(connected:User) RETURN connected.name, length(path) as distance ORDER BY distance, connected.name; </code></pre></div>Depth-First Search (DFS): <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Deep exploration of paths MATCH path = (start:User {id: 123})-[:FOLLOWS*1..5]->(reached:User) RETURN DISTINCT reached.name, length(path) as depth ORDER BY depth DESC, reached.name; </code></pre></div>Cycle Detection: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Find cycles in the graph MATCH path = (n:Node)-[:CONNECTS*]->(n) WHERE length(path) > 1 RETURN path, length(path) as cycle_length ORDER BY cycle_length LIMIT 10; </code></pre></div> <h3 id="flow-and-optimization" class="position-relative d-flex align-items-center group"> Flow and 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="flow-and-optimization" aria-haspopup="dialog" aria-label="Share link: Flow and Optimization"> Share link </button> </h3>Maximum Flow (network capacity): <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Simplified max flow calculation MATCH path = (source:Node {id: 'A'})-[r:PIPE*]->(sink:Node {id: 'B'}) WITH path, reduce(flow = 999999, rel in relationships(path) | CASE WHEN rel.capacity < flow THEN rel.capacity ELSE flow END ) as path_capacity RETURN path, path_capacity ORDER BY path_capacity DESC; </code></pre></div>Minimum Spanning Tree: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Connect all nodes with minimum total edge weight MATCH (n:Location) WITH collect(n) as nodes MATCH path = (a:Location)-[r:ROAD]-(b:Location) WHERE a IN nodes AND b IN nodes RETURN path, r.distance as weight ORDER BY weight; </code></pre></div> <h3 id="anomaly-detection" class="position-relative d-flex align-items-center group"> Anomaly 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="anomaly-detection" aria-haspopup="dialog" aria-label="Share link: Anomaly Detection"> Share link </button> </h3>Unusual Pattern Detection: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Find users with anomalous behavior MATCH (u:User) OPTIONAL MATCH (u)-[:PURCHASED]->(p:Product) WITH u, count(p) as purchase_count, avg(p.price) as avg_spend WITH avg(purchase_count) as avg_purchases, stddev(purchase_count) as stddev_purchases, avg(avg_spend) as global_avg_spend, stddev(avg_spend) as stddev_spend MATCH (u:User) OPTIONAL MATCH (u)-[:PURCHASED]->(p:Product) WITH u, count(p) as user_purchases, avg(p.price) as user_avg_spend, avg_purchases, stddev_purchases, global_avg_spend, stddev_spend WHERE abs(user_purchases - avg_purchases) > 3 * stddev_purchases OR abs(user_avg_spend - global_avg_spend) > 3 * stddev_spend RETURN u.name, user_purchases, user_avg_spend; </code></pre></div>Fraud Ring Detection: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Identify tightly connected suspicious accounts MATCH (suspect:Account {flagged: true})-[:TRANSACTED_WITH*1..2]-(connected:Account) WITH suspect, collect(DISTINCT connected) as ring_members WHERE size(ring_members) > 5 MATCH (m1:Account)-[:TRANSACTED_WITH]-(m2:Account) WHERE m1 IN ring_members AND m2 IN ring_members RETURN suspect.id, ring_members, count(*) as internal_transactions ORDER BY internal_transactions DESC; </code></pre></div> <h3 id="graph-metrics-and-statistics" class="position-relative d-flex align-items-center group"> Graph Metrics and Statistics <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-metrics-and-statistics" aria-haspopup="dialog" aria-label="Share link: Graph Metrics and Statistics"> Share link </button> </h3>Diameter (longest shortest path): <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Calculate graph diameter MATCH path = shortestPath((a:Node)-[*]-(b:Node)) WHERE a < b RETURN max(length(path)) as diameter; </code></pre></div>Density (edge to node ratio): <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Calculate graph density MATCH (n:Node) WITH count(n) as node_count MATCH ()-[r:EDGE]-() RETURN count(r) * 1.0 / (node_count * (node_count - 1)) as density; </code></pre></div>Degree Distribution: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Analyze degree distribution MATCH (n:Node) OPTIONAL MATCH (n)-[r]-(m:Node) WITH n, count(r) as degree RETURN degree, count(n) as node_count ORDER BY degree; </code></pre></div> <h3 id="performance-optimization-for-algorithms" class="position-relative d-flex align-items-center group"> Performance Optimization for 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="performance-optimization-for-algorithms" aria-haspopup="dialog" aria-label="Share link: Performance Optimization for Algorithms"> Share link </button> </h3>Limit Traversal Depth: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Always bound variable-length patterns MATCH path = (a)-[*1..6]-(b) -- Good: bounded -- MATCH path = (a)-[*]-(b) -- Bad: unbounded RETURN path; </code></pre></div>Use Early Filtering: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Filter before expensive traversals MATCH (start:User) WHERE start.active = true -- Filter first AND start.country = 'US' MATCH path = (start)-[:KNOWS*1..3]-(connected:User) RETURN path; </code></pre></div>Leverage Indexes: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Start with indexed lookups CREATE INDEX user_id ON :User(id); MATCH (u:User {id: 123}) -- Uses index MATCH path = (u)-[:FOLLOWS*1..4]->(reached:User) RETURN path; </code></pre></div>Parallel Processing: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Break large computations into batches MATCH (u:User) WHERE u.id >= 0 AND u.id < 1000 -- Batch 1 WITH u MATCH (u)-[:KNOWS]-(friend:User) RETURN u.id, count(friend) as degree; </code></pre></div> <h3 id="use-cases-by-industry" class="position-relative d-flex align-items-center group"> Use Cases by Industry <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="use-cases-by-industry" aria-haspopup="dialog" aria-label="Share link: Use Cases by Industry"> Share link </button> </h3>Social Networks: Influence ranking, friend recommendations, community detection Fraud Detection: Ring identification, anomaly detection, pattern analysis Supply Chain: Shortest paths, bottleneck identification, flow optimization Recommendation Engines: Collaborative filtering, similarity scoring, personalization Network Security: Intrusion path analysis, vulnerability assessment, access patterns Biology: Protein interaction analysis, pathway discovery, disease networks <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>Always bound variable-length paths to prevent explosions</li> <li>Use appropriate indexes for algorithm starting points</li> <li>Consider graph density when choosing algorithms</li> <li>Profile algorithm performance on representative data</li> <li>Implement incremental updates for frequently computed metrics</li> <li>Cache results for expensive computations</li> <li>Use sampling for approximate results on huge graphs</li> <li>Parallelize independent computations across nodes</li> <li>Monitor memory usage for large traversals</li> <li>Validate results on known test cases</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/patterns/" >Query Patterns</a> </li> <li><a href="/tags/performance/" >Performance Optimization</a> </li> <li><a href="/tags/pagerank/" >PageRank Algorithm</a> </li> <li><a href="/tags/community-detection/" >Community Detection</a> </li> <li><a href="/tags/pattern-matching/" >Pattern Matching</a> </li> <li><a href="/tags/analytics/" >Analytics and ML</a> </li> </ul> <h3 id="advanced-algorithm-implementations" class="position-relative d-flex align-items-center group"> Advanced Algorithm Implementations <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-implementations" aria-haspopup="dialog" aria-label="Share link: Advanced Algorithm Implementations"> Share link </button> </h3> <h4 id="all-pairs-shortest-paths-floyd-warshall" class="position-relative d-flex align-items-center group"> All-Pairs Shortest Paths (Floyd-Warshall) <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-pairs-shortest-paths-floyd-warshall" aria-haspopup="dialog" aria-label="Share link: All-Pairs Shortest Paths (Floyd-Warshall)"> Share link </button> </h4>Compute distances between all node pairs for dense graphs: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Initialize distance matrix MATCH (source:Node), (target:Node) WHERE source <> target MERGE (source)-[d:DISTANCE]->(target) SET d.distance = CASE WHEN EXISTS((source)-[:CONNECTED]-(target)) THEN 1 ELSE 999999 END; -- Floyd-Warshall iterations MATCH (i:Node), (j:Node), (k:Node) WHERE i <> j AND j <> k AND i <> k MATCH (i)-[ij:DISTANCE]->(j) MATCH (i)-[ik:DISTANCE]->(k) MATCH (k)-[kj:DISTANCE]->(j) WITH i, j, ij, ik.distance + kj.distance AS new_distance WHERE new_distance < ij.distance SET ij.distance = new_distance; -- Query all-pairs distances MATCH (a:Node {id: $node_a})-[d:DISTANCE]->(b:Node {id: $node_b}) RETURN a.id, b.id, d.distance AS shortest_distance; </code></pre></div>Complexity: O(V³), suitable for V < 1000 Memory: O(V²) for distance matrix Use case: Dense graphs, transitive closure, diameter calculation <h4 id="bellman-ford-algorithm-negative-weights" class="position-relative d-flex align-items-center group"> Bellman-Ford Algorithm (Negative Weights) <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="bellman-ford-algorithm-negative-weights" aria-haspopup="dialog" aria-label="Share link: Bellman-Ford Algorithm (Negative Weights)"> Share link </button> </h4>Handle graphs with negative edge weights: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Initialize distances MATCH (n:Node) SET n.distance = CASE WHEN n.id = $source_id THEN 0 ELSE 999999 END; -- Relax edges V-1 times MATCH (u:Node)-[r:EDGE]->(v:Node) WHERE u.distance + r.weight < v.distance SET v.distance = u.distance + r.weight, v.predecessor = u.id; -- Detect negative cycles MATCH (u:Node)-[r:EDGE]->(v:Node) WHERE u.distance + r.weight < v.distance RETURN 'Negative cycle detected' AS warning, u.id, v.id; -- Extract shortest path MATCH (target:Node {id: $target_id}) WITH target.id AS current_id, [] AS path CALL { WITH current_id, path MATCH (n:Node {id: current_id}) WHERE n.predecessor IS NOT NULL WITH n.predecessor AS pred, path + [current_id] AS new_path RETURN pred AS next_id, new_path AS result_path } RETURN result_path AS shortest_path; </code></pre></div>Complexity: O(V × E) Advantages: Handles negative weights, detects negative cycles Use case: Currency arbitrage, price optimization <h4 id="tarjans-strongly-connected-components" class="position-relative d-flex align-items-center group"> Tarjan&rsquo;s 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="tarjans-strongly-connected-components" aria-haspopup="dialog" aria-label="Share link: Tarjans Strongly Connected Components"> Share link </button> </h4>Find strongly connected components in O(V + E) time: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Initialize node state MATCH (n:Node) SET n.index = null, n.lowlink = null, n.on_stack = false; -- Recursive DFS for SCC detection MATCH (v:Node) WHERE v.index IS NULL CALL { WITH v SET v.index = $current_index, v.lowlink = $current_index, v.on_stack = true WITH v, $current_index + 1 AS next_index MATCH (v)-[:EDGE]->(w:Node) CALL { WITH w, next_index CASE WHEN w.index IS NULL THEN // Recurse SET w.index = next_index WHEN w.on_stack = true THEN // Update lowlink SET v.lowlink = CASE WHEN w.index < v.lowlink THEN w.index ELSE v.lowlink END END } // If v is root of SCC WITH v WHERE v.lowlink = v.index MATCH (w:Node) WHERE w.on_stack = true AND w.index >= v.index SET w.component_id = v.id, w.on_stack = false RETURN v.id AS scc_root }; -- Query component membership MATCH (n:Node) WHERE n.component_id IS NOT NULL RETURN n.component_id AS component, COUNT(n) AS size, COLLECT(n.id) AS members ORDER BY size DESC; </code></pre></div>Applications: Web crawling, social network analysis, compiler optimization <h4 id="edmonds-karp-maximum-flow" class="position-relative d-flex align-items-center group"> Edmonds-Karp Maximum Flow <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="edmonds-karp-maximum-flow" aria-haspopup="dialog" aria-label="Share link: Edmonds-Karp Maximum Flow"> Share link </button> </h4>Compute maximum flow from source to sink: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Initialize residual graph MATCH (u:Node)-[e:EDGE]->(v:Node) MERGE (u)-[forward:RESIDUAL {capacity: e.capacity, flow: 0}]->(v) MERGE (v)-[backward:RESIDUAL {capacity: 0, flow: 0}]->(u); -- Augmenting path search (BFS) WITH $source_id AS source, $sink_id AS sink MATCH path = shortestPath((s:Node {id: source})-[:RESIDUAL*]->(t:Node {id: sink})) WHERE ALL(r IN relationships(path) WHERE r.capacity - r.flow > 0) WITH path, REDUCE(min_cap = 999999, r IN relationships(path) | CASE WHEN r.capacity - r.flow < min_cap THEN r.capacity - r.flow ELSE min_cap END ) AS bottleneck WITH path, bottleneck UNWIND relationships(path) AS edge SET edge.flow = edge.flow + bottleneck WITH path, bottleneck MATCH (u)-[forward:RESIDUAL]->(v) WHERE forward IN relationships(path) MATCH (v)-[backward:RESIDUAL]->(u) SET backward.capacity = backward.capacity + bottleneck; -- Extract max flow value MATCH (:Node {id: $source_id})-[r:RESIDUAL]->() RETURN SUM(r.flow) AS max_flow_value; </code></pre></div>Complexity: O(V × E²) Applications: Network capacity, bipartite matching, airline scheduling <h3 id="production-scale-optimizations" class="position-relative d-flex align-items-center group"> Production-Scale Optimizations <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-scale-optimizations" aria-haspopup="dialog" aria-label="Share link: Production-Scale Optimizations"> Share link </button> </h3> <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>Leverage Geode’s parallel processing for large graphs: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Parallel PageRank with batch updates MATCH (n:Node) WITH COUNT(n) AS total_nodes SET n.pagerank = 1.0 / total_nodes; -- Process in parallel batches MATCH (n:Node) WITH n, n.id % 10 AS partition_id CALL { WITH n, partition_id MATCH (n)-[:EDGE]->(neighbor:Node) WITH neighbor, SUM(n.pagerank / COUNT { (n)-[:EDGE]->() }) AS incoming_rank SET neighbor.pagerank_new = 0.15 + 0.85 * incoming_rank } IN TRANSACTIONS OF 100000 ROWS PER PARTITION (partition_id); -- Parallel strongly-connected component detection MATCH (n:Node) CALL { WITH n MATCH path = (n)-[:EDGE*]->(n) WITH n, COLLECT(DISTINCT [node IN nodes(path) | ID(node)]) AS cycles SET n.scc_candidates = cycles } IN TRANSACTIONS OF 10000 ROWS; </code></pre></div> <h4 id="sampling-and-approximation" class="position-relative d-flex align-items-center group"> Sampling and Approximation <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="sampling-and-approximation" aria-haspopup="dialog" aria-label="Share link: Sampling and Approximation"> Share link </button> </h4>Achieve faster results with approximate algorithms: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Approximate betweenness centrality (sample-based) WITH 100 AS sample_size // Sample 100 random nodes instead of all pairs MATCH (sample:Node) WITH sample ORDER BY rand() LIMIT $sample_size MATCH path = shortestPath((sample)-[:EDGE*]-(target:Node)) WHERE sample <> target WITH nodes(path) AS path_nodes UNWIND path_nodes AS node WHERE node <> path_nodes[0] AND node <> path_nodes[-1] WITH node, COUNT(*) AS sampled_betweenness RETURN node.id, sampled_betweenness * ($total_nodes / $sample_size) AS estimated_betweenness ORDER BY estimated_betweenness DESC; </code></pre></div>Accuracy: ~95% correlation with exact values at 10× speedup <h4 id="incremental-algorithm-updates" class="position-relative d-flex align-items-center group"> Incremental Algorithm 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="incremental-algorithm-updates" aria-haspopup="dialog" aria-label="Share link: Incremental Algorithm Updates"> Share link </button> </h4>Update algorithm results without full recomputation: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Incremental PageRank after edge addition MATCH (u:Node {id: $new_source}), (v:Node {id: $new_target}) MERGE (u)-[:EDGE]->(v); -- Localized update (affected nodes only) MATCH (affected:Node) WHERE affected IN [u, v] OR EXISTS((affected)-[:EDGE*1..2]-(u)) OR EXISTS((affected)-[:EDGE*1..2]-(v)) WITH affected MATCH (affected)-[:EDGE]->(neighbor:Node) WITH neighbor, SUM(affected.pagerank / COUNT { (affected)-[:EDGE]->() }) AS delta SET neighbor.pagerank = neighbor.pagerank + 0.85 * delta, neighbor.needs_full_recompute = false; -- Incremental community detection after node addition MATCH (new_node:Node {id: $new_node_id}) MATCH (new_node)-[:EDGE]-(neighbor:Node) WITH neighbor.community AS candidate_community, COUNT(*) AS connections ORDER BY connections DESC LIMIT 1 SET new_node.community = candidate_community; </code></pre></div> <h4 id="memory-efficient-graph-traversal" class="position-relative d-flex align-items-center group"> Memory-Efficient Graph Traversal <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="memory-efficient-graph-traversal" aria-haspopup="dialog" aria-label="Share link: Memory-Efficient Graph Traversal"> Share link </button> </h4>Handle billion-edge graphs with streaming: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Streaming BFS for large graphs WITH $start_id AS start_id, 0 AS level CALL { WITH start_id, level MATCH (current:Node {id: start_id}) SET current.level = level RETURN current.id AS processed_id } WITH level + 1 AS next_level CALL { WITH next_level MATCH (current:Node)-[:EDGE]->(next:Node) WHERE current.level = next_level - 1 AND next.level IS NULL SET next.level = next_level RETURN COUNT(next) AS nodes_at_level } IN TRANSACTIONS OF 50000 ROWS RETURN next_level AS level, nodes_at_level; </code></pre></div> <h3 id="algorithm-benchmarking-framework" class="position-relative d-flex align-items-center group"> Algorithm Benchmarking Framework <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-benchmarking-framework" aria-haspopup="dialog" aria-label="Share link: Algorithm Benchmarking Framework"> Share link </button> </h3> <h4 id="performance-testing" class="position-relative d-flex align-items-center group"> Performance Testing <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-testing" aria-haspopup="dialog" aria-label="Share link: Performance Testing"> Share link </button> </h4>Benchmark algorithm performance on your data: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Benchmark PageRank iterations WITH datetime() AS start_time MATCH (n:Node) SET n.pagerank = 1.0 / COUNT { MATCH (m:Node) }; // Run 20 iterations WITH start_time, range(1, 20) AS iterations UNWIND iterations AS iter CALL { MATCH (source:Node)-[:EDGE]->(target:Node) WITH target, SUM(source.pagerank / COUNT { (source)-[:EDGE]->() }) AS rank SET target.pagerank_new = 0.15 + 0.85 * rank } MATCH (n:Node) SET n.pagerank = n.pagerank_new REMOVE n.pagerank_new WITH start_time, datetime() AS end_time RETURN duration.between(start_time, end_time).milliseconds AS runtime_ms, runtime_ms / 20.0 AS ms_per_iteration; -- Memory usage profiling CALL dbms.memory.usage() YIELD used, total, peak RETURN used / 1024 / 1024 AS used_mb, total / 1024 / 1024 AS total_mb, peak / 1024 / 1024 AS peak_mb; </code></pre></div> <h4 id="convergence-analysis" class="position-relative d-flex align-items-center group"> Convergence 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="convergence-analysis" aria-haspopup="dialog" aria-label="Share link: Convergence Analysis"> Share link </button> </h4>Monitor algorithm convergence: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Track PageRank convergence WITH [] AS convergence_history MATCH (n:Node) WITH convergence_history + [n.pagerank] AS history // After iteration MATCH (n:Node) WITH history, n.pagerank_new - n.pagerank AS delta WITH AVG(ABS(delta)) AS mean_change, MAX(ABS(delta)) AS max_change, STDDEV(ABS(delta)) AS stddev_change RETURN mean_change, max_change, stddev_change, CASE WHEN mean_change < 0.0001 THEN 'CONVERGED' ELSE 'CONTINUE' END AS status; </code></pre></div> <h3 id="industry-specific-applications" class="position-relative d-flex align-items-center group"> Industry-Specific 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="industry-specific-applications" aria-haspopup="dialog" aria-label="Share link: Industry-Specific Applications"> Share link </button> </h3> <h4 id="financial-networks" class="position-relative d-flex align-items-center group"> Financial 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="financial-networks" aria-haspopup="dialog" aria-label="Share link: Financial Networks"> Share link </button> </h4>Detect systemic risk and contagion: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Bank exposure network analysis MATCH (bank:Bank)-[exp:EXPOSURE]->(counterparty:Bank) WITH bank, SUM(exp.amount) AS total_exposure, bank.capital AS capital WITH bank, total_exposure / capital AS leverage_ratio WHERE leverage_ratio > 10.0 MATCH path = (bank)-[:EXPOSURE*1..3]->(systemic:Bank) WHERE systemic.systemically_important = true RETURN bank.name, leverage_ratio, COUNT(DISTINCT path) AS contagion_paths, SUM([r IN relationships(path) | r.amount]) AS total_risk ORDER BY total_risk DESC; </code></pre></div> <h4 id="supply-chain-optimization" class="position-relative d-flex align-items-center group"> Supply Chain 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="supply-chain-optimization" aria-haspopup="dialog" aria-label="Share link: Supply Chain Optimization"> Share link </button> </h4>Identify bottlenecks and optimize flows: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Critical path analysis MATCH path = (supplier:Supplier)-[:SUPPLIES*]->(manufacturer:Manufacturer) -[:SHIPS*]->(distributor:Distributor) WITH path, REDUCE(time = 0, r IN relationships(path) | time + r.lead_time_days) AS total_time ORDER BY total_time DESC LIMIT 1 RETURN [n IN nodes(path) | n.name] AS critical_path, total_time AS longest_lead_time, [r IN relationships(path) | r.lead_time_days] AS segment_times; -- Bottleneck identification (max flow) MATCH (factory:Factory {id: $factory_id}) MATCH (warehouse:Warehouse {id: $warehouse_id}) CALL algorithms.maxFlow(factory, warehouse, 'SHIPS', 'capacity') YIELD path, flow WITH REDUCE(min_cap = 999999, r IN relationships(path) | CASE WHEN r.capacity < min_cap THEN r.capacity ELSE min_cap END ) AS bottleneck_capacity, path RETURN [n IN nodes(path) | n.name] AS supply_chain_path, bottleneck_capacity, 'Bottleneck at ' + [r IN relationships(path) WHERE r.capacity = bottleneck_capacity][0].name AS bottleneck_location; </code></pre></div> <h4 id="biological-networks" class="position-relative d-flex align-items-center group"> Biological 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="biological-networks" aria-haspopup="dialog" aria-label="Share link: Biological Networks"> Share link </button> </h4>Analyze protein interactions and pathways: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Protein-protein interaction centrality MATCH (protein:Protein) OPTIONAL MATCH (protein)-[:INTERACTS_WITH]-(partner:Protein) WITH protein, COUNT(DISTINCT partner) AS degree, AVG(partner.expression_level) AS avg_partner_expression WHERE degree >= 10 // Hub proteins MATCH path = shortestPath((protein)-[:INTERACTS_WITH*]-(disease:Disease)) RETURN protein.name, degree AS interaction_count, avg_partner_expression, LENGTH(path) AS disease_proximity, protein.function AS biological_role ORDER BY degree DESC, disease_proximity ASC; </code></pre></div> <h3 id="visualization-and-analysis" class="position-relative d-flex align-items-center group"> Visualization and 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="visualization-and-analysis" aria-haspopup="dialog" aria-label="Share link: Visualization and Analysis"> Share link </button> </h3> <h4 id="graph-metric-dashboard" class="position-relative d-flex align-items-center group"> Graph Metric Dashboard <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-metric-dashboard" aria-haspopup="dialog" aria-label="Share link: Graph Metric Dashboard"> Share link </button> </h4>Compute comprehensive graph statistics: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Complete graph analytics dashboard MATCH (n:Node) WITH COUNT(n) AS node_count, COLLECT(n) AS all_nodes MATCH ()-[r:EDGE]-() WITH node_count, all_nodes, COUNT(r) AS edge_count WITH node_count, edge_count, edge_count * 2.0 / (node_count * (node_count - 1)) AS density, edge_count * 1.0 / node_count AS avg_degree MATCH (n:Node) OPTIONAL MATCH (n)-[r:EDGE]-() WITH node_count, edge_count, density, avg_degree, COUNT(r) AS node_degree WITH node_count, edge_count, density, avg_degree, COLLECT(node_degree) AS degree_dist WITH node_count, edge_count, density, avg_degree, degree_dist, percentile_cont(degree_dist, 0.5) AS median_degree, percentile_cont(degree_dist, 0.95) AS p95_degree MATCH path = shortestPath((a:Node)-[:EDGE*]-(b:Node)) WHERE a <> b WITH node_count, edge_count, density, avg_degree, median_degree, p95_degree, MAX(LENGTH(path)) AS diameter, AVG(LENGTH(path)) AS avg_path_length RETURN node_count, edge_count, density, avg_degree, median_degree, p95_degree, diameter, avg_path_length, CASE WHEN avg_path_length / log(node_count) < 2 THEN 'Small World' WHEN density > 0.1 THEN 'Dense' ELSE 'Sparse' END AS graph_type; </code></pre></div> <h4 id="degree-distribution-analysis" class="position-relative d-flex align-items-center group"> Degree Distribution 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="degree-distribution-analysis" aria-haspopup="dialog" aria-label="Share link: Degree Distribution Analysis"> Share link </button> </h4>Identify network topology: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Degree distribution histogram MATCH (n:Node) OPTIONAL MATCH (n)-[r:EDGE]-() WITH n, COUNT(r) AS degree WITH degree, COUNT(n) AS frequency ORDER BY degree WITH COLLECT({degree: degree, count: frequency}) AS distribution RETURN distribution, CASE WHEN distribution[-1].count > distribution[0].count THEN 'Power Law (Scale-Free)' WHEN AVG([d IN distribution | ABS(d.count - AVG([x IN distribution | x.count]))]) < 2 THEN 'Regular Network' ELSE 'Random Network' END AS topology_type; </code></pre></div> <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 Algorithms: Practical Examples in Network Science</li> <li>Network Analysis with GQL: Advanced Query Patterns and Optimization</li> <li>Scalable Graph Processing: Distributed Algorithms for Billion-Node Graphs</li> <li>Machine Learning on Graphs: Graph Neural Networks and Embedding Techniques</li> <li>Social Network Analysis: Community Detection and Influence Propagation</li> <li>Graph Algorithm Complexity: Theoretical Foundations and Practical Bounds</li> <li>Production Graph Analytics: Real-Time Processing at Scale</li> </ul> <h3 id="related-topics-1" 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-1" aria-haspopup="dialog" aria-label="Share link: Related Topics"> Share link </button> </h3><ul> <li><a href="/tags/pattern-matching/" >Pattern Matching</a> </li> <li><a href="/tags/query-optimization/" >Query Optimization</a> </li> <li><a href="/tags/performance/" >Performance Optimization</a> </li> <li><a href="/tags/analytics/" >Analytics</a> </li> </ul> Browse the tagged content below to discover documentation, tutorials, and guides for implementing graph algorithms in your Geode applications.

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