Category: Graph Algorithms and Analytics

The Graph Algorithms and Analytics category provides comprehensive documentation for implementing advanced computational techniques on graph data using Geode. This collection covers everything from classical graph algorithms to modern machine learning approaches, enabling you to extract deep insights from connected data. <h3 id="introduction-to-graph-algorithms" class="position-relative d-flex align-items-center group"> Introduction to 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="introduction-to-graph-algorithms" aria-haspopup="dialog" aria-label="Share link: Introduction to 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 database queries that retrieve data, graph algorithms analyze the structure and relationships within your data to discover patterns, measure importance, identify communities, and predict connections. These techniques are essential for modern applications in social networks, fraud detection, recommendation systems, knowledge graphs, and network analysis. Geode provides native support for executing graph algorithms through its ISO-standard GQL query language, offering both built-in operations and the flexibility to implement custom algorithms using GQL’s powerful pattern matching and aggregation capabilities. <h3 id="core-algorithm-categories" class="position-relative d-flex align-items-center group"> Core 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="core-algorithm-categories" aria-haspopup="dialog" aria-label="Share link: Core Algorithm Categories"> Share link </button> </h3> <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>Centrality algorithms identify the most important nodes in a graph based on various criteria. PageRank measures influence by analyzing the quality and quantity of incoming relationships, making it ideal for ranking web pages, identifying key influencers in social networks, or finding critical infrastructure nodes. Betweenness Centrality identifies nodes that act as bridges between different parts of the graph, useful for finding bottlenecks or key intermediaries. Degree Centrality simply counts connections, while Closeness Centrality measures how quickly information can spread from a node. In Geode, you can compute centrality using aggregation queries: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">// Find most connected users (degree centrality) MATCH (u:User)-[r]-() RETURN u.name, COUNT(r) AS connections ORDER BY connections DESC LIMIT 10 </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>Community detection algorithms identify clusters of nodes that are more densely connected to each other than to the rest of the graph. Label Propagation is a fast, scalable approach where nodes adopt labels from their neighbors through iterative voting. Louvain Modularity optimizes for modularity, a measure of community structure quality. Weakly Connected Components finds isolated groups with no connections between them. These algorithms are crucial for market segmentation, detecting fraud rings, organizing knowledge bases, and understanding social group dynamics. <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python"># Python example: Finding communities through pattern analysis import geode_client client = geode_client.open_database("localhost:3141") async with client.connection() as client: # Find tightly connected user groups result, _ = await client.query(""" MATCH (u1:User)-[:FOLLOWS]->(u2:User) WHERE EXISTS { MATCH (u2)-[:FOLLOWS]->(u1) } RETURN u1.community, COUNT(*) AS size GROUP BY u1.community ORDER BY size DESC """) </code></pre></div> <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>Pathfinding algorithms discover routes through the graph. Shortest Path finds the minimum-hop route between nodes, essential for navigation, network routing, and supply chain optimization. Dijkstra’s Algorithm extends this to weighted graphs, considering relationship costs. All Shortest Paths finds all minimal routes, useful when multiple equivalent options exist. Geode’s GQL implementation provides native pathfinding through path patterns: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">// Find shortest path between people MATCH path = SHORTEST (a:Person {name: 'Alice'})-[:KNOWS*]-(b:Person {name: 'Bob'}) RETURN path, LENGTH(path) AS hops </code></pre></div> <h4 id="graph-neural-networks-and-embeddings" class="position-relative d-flex align-items-center group"> Graph Neural Networks and Embeddings <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-and-embeddings" aria-haspopup="dialog" aria-label="Share link: Graph Neural Networks and Embeddings"> Share link </button> </h4>Graph Neural Networks (GNNs) learn vector representations of nodes that capture both their attributes and structural position in the graph. Node2Vec creates embeddings through random walks, enabling traditional machine learning on graph data. Graph Convolutional Networks aggregate information from neighborhoods to learn representations. Geode supports storing and querying vector embeddings, enabling similarity search and machine learning workflows: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python"># Store node embeddings for similarity search await client.execute(""" MATCH (p:Product {id: $product_id}) SET p.embedding = $embedding_vector """, {"product_id": 123, "embedding_vector": [0.23, 0.45, -0.12, ...]}) # Find similar products using cosine similarity result, _ = await client.query(""" MATCH (target:Product {id: $id}) MATCH (candidate:Product) WHERE candidate.id <> $id RETURN candidate.name, vector.cosine_similarity(target.embedding, candidate.embedding) AS similarity ORDER BY similarity DESC LIMIT 5 """, {"id": 123}) </code></pre></div> <h3 id="real-time-analytics" class="position-relative d-flex align-items-center group"> Real-Time Analytics <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-time-analytics" aria-haspopup="dialog" aria-label="Share link: Real-Time Analytics"> Share link </button> </h3>Modern applications require analytics on live, changing data. Geode’s MVCC (Multi-Version Concurrency Control) architecture enables real-time queries without blocking writes, making it ideal for streaming analytics, live dashboards, and operational intelligence. Real-time pattern detection identifies emerging trends as data arrives: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">// Detect unusual activity patterns in real-time MATCH (u:User)-[:TRANSACTION]->(m:Merchant) WHERE m.timestamp > current_timestamp() - INTERVAL '5' MINUTE GROUP BY u.id HAVING COUNT(*) > u.avg_transactions_per_5min * 3 RETURN u.id, u.name, COUNT(*) AS suspicious_activity </code></pre></div> <h3 id="fraud-detection-and-anomaly-detection" class="position-relative d-flex align-items-center group"> Fraud Detection and 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="fraud-detection-and-anomaly-detection" aria-haspopup="dialog" aria-label="Share link: Fraud Detection and Anomaly Detection"> Share link </button> </h3>Graph algorithms excel at fraud detection because fraudsters create recognizable patterns in relationship data. Ring detection identifies circular money flows, velocity checks measure transaction speed, and network analysis reveals organized fraud networks that would be invisible in traditional databases. <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">// Detect potential fraud rings MATCH (a:Account)-[:TRANSFER]->(b:Account)-[:TRANSFER]->(c:Account) WHERE c.id = a.id AND edge_timestamp(a, b) > current_timestamp() - INTERVAL '1' DAY RETURN a.id, b.id, c.id, SUM(edge_amount) AS total_amount </code></pre></div>Anomaly detection uses statistical measures and machine learning to identify outliers: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python"># Detect accounts with unusual transaction patterns result, _ = await client.query(""" MATCH (a:Account)-[t:TRANSACTION]->() WITH a, AVG(t.amount) AS avg_amount, STDDEV(t.amount) AS stddev_amount, COUNT(t) AS transaction_count WHERE stddev_amount > 0 MATCH (a)-[t:TRANSACTION]->() WHERE ABS(t.amount - avg_amount) > 3 * stddev_amount RETURN a.id, t.amount, avg_amount, stddev_amount """) </code></pre></div> <h3 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> </h3>Graph-based recommendations leverage network structure to suggest relevant items. Collaborative filtering finds users with similar taste graphs and recommends items they’ve liked. Content-based filtering uses node properties and embeddings. Hybrid approaches combine both for superior results. <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">// Collaborative filtering recommendations MATCH (me:User {id: $user_id})-[:LIKES]->(item) <-[:LIKES]-(similar:User) -[:LIKES]->(recommendation) WHERE NOT EXISTS { MATCH (me)-[:LIKES]->(recommendation) } RETURN recommendation.title, COUNT(similar) AS score ORDER BY score DESC LIMIT 10 </code></pre></div> <h3 id="performance-considerations" class="position-relative d-flex align-items-center group"> Performance Considerations <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-considerations" aria-haspopup="dialog" aria-label="Share link: Performance Considerations"> Share link </button> </h3>When implementing graph algorithms in Geode: <ol> <li>Use indexes strategically: Create indexes on node labels and frequently queried properties to accelerate pattern matching</li> <li>Leverage query profiling: Use <code>PROFILE</code> to understand query execution and optimize bottlenecks</li> <li>Consider materialization: For frequently computed metrics, store results as node properties and update incrementally</li> <li>Partition large computations: Break algorithms into smaller chunks using pagination or time windows</li> <li>Utilize prepared statements: Pre-compile complex analytical queries for better performance</li> </ol> <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Profile a centrality computation PROFILE MATCH (n:Node)-[r]-() RETURN n.id, COUNT(r) AS degree ORDER BY degree DESC </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>Start simple: Begin with basic aggregations and pattern matching before implementing complex algorithms. Many insights can be discovered through straightforward queries. Validate results: Compare algorithm outputs against known ground truth when possible, especially for machine learning applications. Monitor performance: Track query execution times and resource usage as your graph grows. What works at 1,000 nodes may need optimization at 1,000,000. Document your models: Graph algorithms depend heavily on how you model relationships. Document which relationship types mean what and how they should be traversed. Combine algorithms: The most powerful insights often come from combining multiple techniques - for example, using community detection to partition the graph, then running PageRank within each community. <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/machine-learning/" >Machine Learning</a> - Integration with ML frameworks</li> <li><a href="/tags/pagerank/" >PageRank</a> - Importance ranking algorithm</li> <li><a href="/tags/community-detection/" >Community Detection</a> - Finding clusters in graphs</li> <li><a href="/tags/fraud-detection/" >Fraud Detection</a> - Detecting fraudulent patterns</li> <li><a href="/tags/recommendations/" >Recommendations</a> - Building recommendation engines</li> <li><a href="/tags/real-time-analytics/" >Real-Time Analytics</a> - Streaming graph analytics</li> <li><a href="/tags/anomaly-detection/" >Anomaly Detection</a> - Identifying unusual patterns</li> <li><a href="/categories/query-optimization/" >Performance Optimization</a> - Optimizing analytical queries</li> </ul> <h3 id="advanced-algorithm-implementation" class="position-relative d-flex align-items-center group"> Advanced 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="advanced-algorithm-implementation" aria-haspopup="dialog" aria-label="Share link: Advanced Algorithm Implementation"> Share link </button> </h3> <h4 id="implementing-custom-algorithms" class="position-relative d-flex align-items-center group"> Implementing Custom 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="implementing-custom-algorithms" aria-haspopup="dialog" aria-label="Share link: Implementing Custom Algorithms"> Share link </button> </h4>While Geode provides built-in implementations of common algorithms, many use cases require custom analytics tailored to specific domains. GQL’s pattern matching and aggregation capabilities enable implementing sophisticated algorithms directly in queries. Iterative Computation with WITH Clauses <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Simplified PageRank iteration WITH 0.85 AS damping_factor MATCH (n:Node) SET n.rank = 1.0 // Iterate multiple times WITH damping_factor MATCH (n:Node)<-[r]-(m:Node) WITH n, damping_factor, SUM(m.rank / degree(m)) AS incoming_rank SET n.rank = (1 - damping_factor) + damping_factor * incoming_rank </code></pre></div>Breadth-First Search Implementation <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python">async def bfs_traversal(client, start_id, max_depth=5): """Implement BFS using iterative queries.""" visited = set([start_id]) current_level = [start_id] for depth in range(max_depth): if not current_level: break result, _ = await client.query(""" MATCH (n)-[:CONNECTED]-(neighbor) WHERE n.id IN $current_ids AND NOT neighbor.id IN $visited RETURN DISTINCT neighbor.id AS id """, {"current_ids": current_level, "visited": list(visited)}) next_level = [] for row in result.rows: next_level.append(row['id']) visited.add(row['id']) current_level = next_level return visited </code></pre></div> <h4 id="graph-sampling-and-statistics" class="position-relative d-flex align-items-center group"> Graph Sampling 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-sampling-and-statistics" aria-haspopup="dialog" aria-label="Share link: Graph Sampling and Statistics"> Share link </button> </h4>For very large graphs, computing exact metrics may be prohibitive. Sampling techniques provide approximate results with bounded error. <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Random node sampling for statistics MATCH (n:User) WHERE random() < 0.01 // 1% sample WITH COUNT(n) AS sample_size, AVG(degree(n)) AS avg_degree, STDDEV(degree(n)) AS stddev_degree RETURN sample_size * 100 AS estimated_total, avg_degree, stddev_degree </code></pre></div>Random Walk Sampling <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Random walk for graph exploration MATCH path = (start:Node {id: $start_id})-[:EDGE*10]->(end) WHERE ALL (r IN relationships(path) WHERE random() > 0.5) RETURN nodes(path), length(path) </code></pre></div> <h3 id="temporal-graph-analytics" class="position-relative d-flex align-items-center group"> Temporal Graph Analytics <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="temporal-graph-analytics" aria-haspopup="dialog" aria-label="Share link: Temporal Graph Analytics"> Share link </button> </h3>Temporal graphs capture how relationships evolve over time, enabling analysis of dynamic networks. <h4 id="time-windowed-analysis" class="position-relative d-flex align-items-center group"> Time-Windowed 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="time-windowed-analysis" aria-haspopup="dialog" aria-label="Share link: Time-Windowed Analysis"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Analyze community evolution over time windows WITH DATE '2025-01-01' AS window_start, DATE '2025-02-01' AS window_end MATCH (u1:User)-[r:INTERACTION]->(u2:User) WHERE r.timestamp >= window_start AND r.timestamp < window_end WITH u1.community AS community, COUNT(DISTINCT r) AS interactions RETURN community, interactions, interactions / 31.0 AS daily_avg ORDER BY interactions DESC </code></pre></div> <h4 id="change-detection" class="position-relative d-flex align-items-center group"> Change 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="change-detection" aria-haspopup="dialog" aria-label="Share link: Change Detection"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Detect nodes with changing centrality MATCH (n:Node) WITH n, n.centrality_last_week AS old_centrality, calculate_centrality(n) AS new_centrality WHERE ABS(new_centrality - old_centrality) / old_centrality > 0.5 RETURN n.id, old_centrality, new_centrality, (new_centrality - old_centrality) / old_centrality AS pct_change ORDER BY ABS(pct_change) DESC </code></pre></div> <h3 id="machine-learning-integration-patterns" class="position-relative d-flex align-items-center group"> Machine Learning Integration 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="machine-learning-integration-patterns" aria-haspopup="dialog" aria-label="Share link: Machine Learning Integration Patterns"> Share link </button> </h3> <h4 id="feature-engineering-from-graphs" class="position-relative d-flex align-items-center group"> Feature Engineering from Graphs <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="feature-engineering-from-graphs" aria-haspopup="dialog" aria-label="Share link: Feature Engineering from Graphs"> Share link </button> </h4>Graph structure provides rich features for machine learning models. <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python">async def extract_node_features(client, node_id): """Extract graph-based features for ML.""" features, _ = await client.query(""" MATCH (n {id: $node_id}) OPTIONAL MATCH (n)-[r]-() WITH n, COUNT(DISTINCT r) AS degree, COUNT{(n)-[:FRIEND]-()} AS friend_count, COUNT{(n)-[:POSTED]->()} AS post_count OPTIONAL MATCH (n)-[:FRIEND*2]-(foaf) WITH n, degree, friend_count, post_count, COUNT(DISTINCT foaf) AS network_size RETURN degree, friend_count, post_count, network_size, friend_count::FLOAT / NULLIF(degree, 0) AS friend_ratio """, {"node_id": node_id}) return features.rows[0] if features.rows else None </code></pre></div> <h4 id="graph-embedding-training" class="position-relative d-flex align-items-center group"> Graph Embedding Training <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-training" aria-haspopup="dialog" aria-label="Share link: Graph Embedding Training"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python">import numpy as np from geode_client import Client async def train_node2vec_embeddings(client, dimensions=128): """Generate Node2Vec embeddings.""" # Generate random walks walks = [] result, _ = await client.query(""" MATCH (start:Node) MATCH path = (start)-[:EDGE*10..20]-(end) RETURN [n IN nodes(path) | n.id] AS walk LIMIT 10000 """) for row in result.rows: walks.append(row['walk']) # Train Word2Vec on walks (node sequences) from gensim.models import Word2Vec model = Word2Vec(walks, vector_size=dimensions, window=5, min_count=1) # Store embeddings back in graph for node_id in model.wv.index_to_key: embedding = model.wv[node_id].tolist() await client.execute(""" MATCH (n:Node {id: $node_id}) SET n.embedding = $embedding """, {"node_id": int(node_id), "embedding": embedding}) </code></pre></div> <h3 id="performance-optimization-strategies" class="position-relative d-flex align-items-center group"> Performance Optimization Strategies <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-strategies" aria-haspopup="dialog" aria-label="Share link: Performance Optimization Strategies"> Share link </button> </h3> <h4 id="query-optimization-for-algorithms" class="position-relative d-flex align-items-center group"> Query 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="query-optimization-for-algorithms" aria-haspopup="dialog" aria-label="Share link: Query Optimization for Algorithms"> Share link </button> </h4>Materialized Views for Repeated Computations <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Pre-compute and store degree centrality MATCH (n:Node)-[r]-() WITH n, COUNT(r) AS degree SET n.degree = degree -- Later queries use pre-computed values MATCH (n:Node) WHERE n.degree > 10 RETURN n.id, n.degree </code></pre></div>Incremental Updates Instead of recomputing metrics from scratch, update them incrementally: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python">async def update_centrality_incremental(client, new_edge_source, new_edge_target): """Update centrality scores incrementally when edge is added.""" await client.execute(""" MATCH (source {id: $source}), (target {id: $target}) SET source.degree = COALESCE(source.degree, 0) + 1, target.degree = COALESCE(target.degree, 0) + 1 """, {"source": new_edge_source, "target": new_edge_target}) </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><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python">import asyncio async def parallel_community_detection(client, communities): """Run PageRank on multiple communities in parallel.""" tasks = [] for community_id in communities: task = compute_pagerank_for_community(client, community_id) tasks.append(task) results = await asyncio.gather(*tasks) return dict(zip(communities, results)) async def compute_pagerank_for_community(client, community_id): """Compute PageRank within a single community.""" result, _ = await client.query(""" MATCH (n:Node {community: $community_id})-[r]->() WITH n, COUNT(r) AS out_degree RETURN n.id, out_degree """, {"community_id": community_id}) # PageRank computation logic here return await process_pagerank(result) </code></pre></div> <h3 id="graph-algorithm-benchmarking" class="position-relative d-flex align-items-center group"> Graph Algorithm Benchmarking <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-algorithm-benchmarking" aria-haspopup="dialog" aria-label="Share link: Graph Algorithm Benchmarking"> 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><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python">import time import statistics async def benchmark_algorithm(client, algorithm_query, params, iterations=10): """Benchmark graph algorithm performance.""" timings = [] for i in range(iterations): start = time.perf_counter() await client.execute(algorithm_query, params) end = time.perf_counter() timings.append(end - start) return { 'mean': statistics.mean(timings), 'median': statistics.median(timings), 'stddev': statistics.stdev(timings), 'min': min(timings), 'max': max(timings) } </code></pre></div> <h4 id="scalability-analysis" class="position-relative d-flex align-items-center group"> Scalability 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="scalability-analysis" aria-haspopup="dialog" aria-label="Share link: Scalability Analysis"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Profile algorithm performance at different scales PROFILE MATCH (n:Node)-[r:EDGE*1..5]-(m:Node) WHERE n.id = $start_id RETURN COUNT(DISTINCT m) AS reachable_nodes, COUNT(r) AS total_paths </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="bioinformatics-protein-interaction-networks" class="position-relative d-flex align-items-center group"> Bioinformatics: Protein Interaction 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="bioinformatics-protein-interaction-networks" aria-haspopup="dialog" aria-label="Share link: Bioinformatics: Protein Interaction Networks"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Find proteins in same pathway MATCH (p1:Protein {name: $protein_name})-[:INTERACTS_WITH*1..3]-(p2:Protein) -[:PART_OF]->(pathway:Pathway) RETURN pathway.name, COUNT(DISTINCT p2) AS proteins_in_pathway ORDER BY proteins_in_pathway DESC </code></pre></div> <h4 id="transportation-route-optimization" class="position-relative d-flex align-items-center group"> Transportation: Route 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="transportation-route-optimization" aria-haspopup="dialog" aria-label="Share link: Transportation: Route Optimization"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Find optimal route with capacity constraints MATCH path = SHORTEST (start:Location {name: $origin}) -[:ROUTE*]-> (end:Location {name: $destination}) WHERE ALL (r IN relationships(path) WHERE r.capacity >= $required_capacity) RETURN path, REDUCE(cost = 0, r IN relationships(path) | cost + r.distance) AS total_distance </code></pre></div> <h4 id="cybersecurity-attack-graph-analysis" class="position-relative d-flex align-items-center group"> Cybersecurity: Attack Graph 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="cybersecurity-attack-graph-analysis" aria-haspopup="dialog" aria-label="Share link: Cybersecurity: Attack Graph Analysis"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Identify critical vulnerabilities in attack paths MATCH path = (attacker:ExternalNode)-[:EXPLOITS*]->(target:CriticalAsset) WITH path, [n IN nodes(path) WHERE n:Vulnerability] AS vulnerabilities RETURN path, vulnerabilities, length(path) AS attack_steps ORDER BY length(path) LIMIT 10 </code></pre></div> <h3 id="visualization-and-exploration" class="position-relative d-flex align-items-center group"> Visualization and Exploration <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-exploration" aria-haspopup="dialog" aria-label="Share link: Visualization and Exploration"> Share link </button> </h3>While Geode focuses on data storage and querying, visualization tools help explore algorithm results. <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python">async def export_for_visualization(client, community_id): """Export subgraph for visualization tools.""" result, _ = await client.query(""" MATCH (n:Node {community: $community_id})-[r]-(m:Node {community: $community_id}) RETURN COLLECT(DISTINCT n) AS nodes, COLLECT(DISTINCT r) AS relationships """, {"community_id": community_id}) data = result.rows[0] if result.rows else None # Export to formats like GraphML, GEXF, or D3.js JSON return convert_to_graphml(data['nodes'], data['relationships']) </code></pre></div> <h3 id="error-handling-and-validation" class="position-relative d-flex align-items-center group"> Error Handling and Validation <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="error-handling-and-validation" aria-haspopup="dialog" aria-label="Share link: Error Handling and Validation"> Share link </button> </h3><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-python" data-lang="python">import asyncio from geode_client import QueryError async def robust_algorithm_execution(client, query, params): """Execute algorithm with proper error handling.""" try: result, _ = await client.query(query, params) return result except QueryError as e: if "timeout" in str(e).lower(): # Retry with increased timeout result, _ = await asyncio.wait_for( client.query(query, params), timeout=60 ) return result elif "memory" in str(e).lower(): # Suggest reducing dataset raise ValueError("Graph too large, consider sampling") else: raise </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><a href="/docs/gql-reference/pattern-matching/" >GQL Pattern Matching</a> - Foundation for graph algorithms</li> <li><a href="/docs/gql-reference/aggregations/" >Aggregation Functions</a> - Statistical computations</li> <li><a href="/tags/vector-search/" >Vector Search</a> - Similarity search and embeddings</li> <li><a href="/tags/profiling/" >Query Profiling</a> - Understanding algorithm performance</li> <li><a href="/categories/best-practices/" >Best Practices</a> - Optimization techniques</li> <li><a href="/docs/query/performance-tuning/" >Performance Tuning</a> - Query optimization guide</li> <li><a href="/tags/temporal/" >Temporal Graphs</a> - Time-aware graph analytics</li> </ul>

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