Graph Algorithms and Analytics

<h2 id="graph-algorithms-and-analytics" class="position-relative d-flex align-items-center group"> Graph Algorithms and 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="graph-algorithms-and-analytics" aria-haspopup="dialog" aria-label="Share link: Graph Algorithms and Analytics"> 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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Use cases: <ul> <li>Influence ranking in social networks</li> <li>Citation importance in academic graphs</li> <li>Website ranking</li> </ul> Query: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Compute PageRank CALL graph.pageRank('SocialNetwork', { relationship_type: 'KNOWS', iterations: 20, damping_factor: 0.85 }) YIELD node, score RETURN node.name AS person, score ORDER BY score DESC; </code></pre></div>Expected output: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-fallback" data-lang="fallback">person | score ---------|------- Charlie | 0.215 Bob | 0.178 Alice | 0.172 Diana | 0.158 Eve | 0.142 Frank | 0.135 </code></pre></div>Interpretation: Charlie has highest PageRank (central position, connected to Bob, Alice, and Diana). <h4 id="betweenness-centrality" class="position-relative d-flex align-items-center group"> Betweenness Centrality <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="betweenness-centrality" aria-haspopup="dialog" aria-label="Share link: Betweenness Centrality"> Share link </button> </h4>Measures how often a node appears on shortest paths between other nodes. Use cases: <ul> <li>Bottleneck identification</li> <li>Bridge detection in networks</li> <li>Information flow control points</li> </ul> Query: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">CALL graph.betweenness('SocialNetwork', { relationship_type: 'KNOWS' }) YIELD node, score RETURN node.name AS person, score ORDER BY score DESC; </code></pre></div>Expected output: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-fallback" data-lang="fallback">person | score ---------|------- Charlie | 6.0 Diana | 4.0 Bob | 2.0 Eve | 2.0 Alice | 0.0 Frank | 0.0 </code></pre></div>Interpretation: Charlie is on the most shortest paths (acts as bridge between Alice/Bob cluster and Diana/Eve/Frank cluster). <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>Measures average distance to all other nodes. Use cases: <ul> <li>Access efficiency</li> <li>Broadcast source selection</li> <li>Epidemic spread analysis</li> </ul> Query: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">CALL graph.closeness('SocialNetwork', { relationship_type: 'KNOWS' }) YIELD node, score RETURN node.name AS person, score ORDER BY score 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> <h4 id="louvain-algorithm" class="position-relative d-flex align-items-center group"> Louvain Algorithm <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="louvain-algorithm" aria-haspopup="dialog" aria-label="Share link: Louvain Algorithm"> Share link </button> </h4>Detects communities (clusters of densely connected nodes). Use cases: <ul> <li>Customer segmentation</li> <li>Topic clustering</li> <li>Organizational structure detection</li> </ul> Query: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">CALL graph.louvain('SocialNetwork', { relationship_type: 'KNOWS', resolution: 1.0 }) YIELD node, community RETURN community, COLLECT(node.name) AS members ORDER BY community; </code></pre></div>Expected output: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-fallback" data-lang="fallback">community | members ----------|------------------------ 1 | ["Alice", "Bob", "Charlie"] 2 | ["Diana", "Eve", "Frank"] </code></pre></div>Interpretation: Two communities detected (left cluster and right cluster). <h4 id="label-propagation" class="position-relative d-flex align-items-center group"> Label Propagation <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="label-propagation" aria-haspopup="dialog" aria-label="Share link: Label Propagation"> Share link </button> </h4>Fast community detection via label spreading. Query: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">CALL graph.labelPropagation('SocialNetwork', { relationship_type: 'KNOWS', iterations: 10 }) YIELD node, community RETURN community, COLLECT(node.name) AS members ORDER BY community; </code></pre></div> <h3 id="shortest-path-algorithms" class="position-relative d-flex align-items-center group"> Shortest Path 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="shortest-path-algorithms" aria-haspopup="dialog" aria-label="Share link: Shortest Path Algorithms"> Share link </button> </h3> <h4 id="dijkstras-shortest-path" class="position-relative d-flex align-items-center group"> Dijkstra&rsquo;s 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="dijkstras-shortest-path" aria-haspopup="dialog" aria-label="Share link: Dijkstras Shortest Path"> Share link </button> </h4>Finds shortest path between two nodes. Query: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Shortest path from Alice to Frank MATCH path = shortestPath( (a:Person {name: "Alice"})-[:KNOWS*]-(f:Person {name: "Frank"}) ) RETURN [n IN nodes(path) | n.name] AS path_nodes, length(path) AS hops; </code></pre></div>Expected output: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-fallback" data-lang="fallback">path_nodes | hops ----------------------------------------|------ ["Alice", "Charlie", "Diana", "Eve", "Frank"] | 4 </code></pre></div> <h4 id="all-shortest-paths" class="position-relative d-flex align-items-center group"> All 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="all-shortest-paths" aria-haspopup="dialog" aria-label="Share link: All Shortest Paths"> Share link </button> </h4>Finds all shortest paths (when multiple exist). <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">MATCH path = allShortestPaths( (a:Person {name: "Alice"})-[:KNOWS*]-(d:Person {name: "Diana"}) ) RETURN [n IN nodes(path) | n.name] AS path_nodes, length(path) AS hops; </code></pre></div>Expected output: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-fallback" data-lang="fallback">path_nodes | hops ----------------------------|------ ["Alice", "Charlie", "Diana"] | 2 ["Alice", "Bob", "Charlie", "Diana"] | 3 </code></pre></div> <h3 id="ml-graph-embeddings" class="position-relative d-flex align-items-center group"> ML Graph 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="ml-graph-embeddings" aria-haspopup="dialog" aria-label="Share link: ML Graph Embeddings"> Share link </button> </h3>From <code>ML_GRAPH_EMBEDDINGS.md</code>: Graph embeddings convert nodes into dense vectors capturing structural and semantic information. <h4 id="node2vec" class="position-relative d-flex align-items-center group"> Node2Vec <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="node2vec" aria-haspopup="dialog" aria-label="Share link: Node2Vec"> Share link </button> </h4>Random walk-based embedding generation. Parameters: <ul> <li><code>dimensions</code>: Embedding dimension (e.g., 128)</li> <li><code>walk_length</code>: Length of random walks (e.g., 80)</li> <li><code>num_walks</code>: Walks per node (e.g., 10)</li> <li><code>p</code>: Return parameter (1.0 = balanced)</li> <li><code>q</code>: In-out parameter (1.0 = balanced)</li> </ul> Query: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">CALL graph.node2vec('SocialNetwork', { relationship_type: 'KNOWS', dimensions: 128, walk_length: 80, num_walks: 10, p: 1.0, q: 1.0 }) YIELD node, embedding WITH node, embedding MATCH (n:Person) WHERE n.id = node.id SET n.embedding = embedding; -- Verify embeddings created MATCH (p:Person) RETURN p.name, p.embedding[0..5] AS embedding_sample; </code></pre></div>Output: Each Person node now has 128-dimensional embedding. <h4 id="graphsage" class="position-relative d-flex align-items-center group"> GraphSAGE <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="graphsage" aria-haspopup="dialog" aria-label="Share link: GraphSAGE"> Share link </button> </h4>Graph Sampling and Aggregation for inductive embeddings. Aggregation strategies: <ul> <li><code>mean</code> - Average neighbor features</li> <li><code>pool</code> - Max pooling</li> <li><code>lstm</code> - LSTM aggregation</li> </ul> Query: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">CALL graph.graphSAGE('SocialNetwork', { relationship_type: 'KNOWS', dimensions: 128, num_samples: 25, aggregator: 'mean' }) YIELD node, embedding WITH node, embedding MATCH (n:Person) WHERE n.id = node.id SET n.embedding = embedding; </code></pre></div> <h4 id="deepwalk" class="position-relative d-flex align-items-center group"> DeepWalk <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="deepwalk" aria-haspopup="dialog" aria-label="Share link: DeepWalk"> Share link </button> </h4>Simplified Node2Vec (p=1, q=1). Query: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">CALL graph.deepWalk('SocialNetwork', { relationship_type: 'KNOWS', dimensions: 128, walk_length: 80, num_walks: 10 }) YIELD node, embedding WITH node, embedding MATCH (n:Person) WHERE n.id = node.id SET n.embedding = embedding; </code></pre></div> <h3 id="vector-similarity-search" class="position-relative d-flex align-items-center group"> Vector Similarity 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="vector-similarity-search" aria-haspopup="dialog" aria-label="Share link: Vector Similarity Search"> Share link </button> </h3>Once embeddings are generated, use vector similarity for: <ul> <li>Similar node discovery</li> <li>Recommendations</li> <li>Anomaly detection (outliers)</li> </ul> <h4 id="create-vector-index" class="position-relative d-flex align-items-center group"> Create Vector 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="create-vector-index" aria-haspopup="dialog" aria-label="Share link: Create Vector Index"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Create HNSW index on embeddings CREATE INDEX person_embedding_idx ON Person(embedding) USING vector; </code></pre></div> <h4 id="find-similar-nodes" class="position-relative d-flex align-items-center group"> Find Similar Nodes <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="find-similar-nodes" aria-haspopup="dialog" aria-label="Share link: Find Similar Nodes"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Find people similar to Alice MATCH (alice:Person {name: "Alice"}) MATCH (p:Person) WHERE p.id <> alice.id AND vector_distance_cosine(p.embedding, alice.embedding) < 0.5 RETURN p.name, vector_distance_cosine(p.embedding, alice.embedding) AS similarity ORDER BY similarity ASC LIMIT 5; </code></pre></div>Expected output: Bob and Charlie (close neighbors) will have lowest distance. <h4 id="recommendation-system" class="position-relative d-flex align-items-center group"> Recommendation System <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-system" aria-haspopup="dialog" aria-label="Share link: Recommendation System"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Recommend people similar to Alice's friends MATCH (alice:Person {name: "Alice"})-[:KNOWS]->(friend) WITH COLLECT(friend) AS friends MATCH (p:Person) WHERE NOT p IN friends AND p.name <> "Alice" WITH p, friends UNWIND friends AS f WITH p, AVG(vector_distance_cosine(p.embedding, f.embedding)) AS avg_similarity WHERE avg_similarity < 0.6 RETURN p.name, avg_similarity ORDER BY avg_similarity ASC LIMIT 5; </code></pre></div>Interpretation: Recommend people similar to Alice’s existing friends (friend-of-friend recommendations). <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>From <code>GRAPH_ALGORITHM_PERFORMANCE_ENHANCEMENTS.md</code>: <h4 id="simd-acceleration" class="position-relative d-flex align-items-center group"> SIMD Acceleration <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="simd-acceleration" aria-haspopup="dialog" aria-label="Share link: SIMD Acceleration"> Share link </button> </h4>Vector operations use SIMD instructions: <ul> <li>Distance calculations: AVX2/AVX-512 vectorized operations</li> <li>Aggregations: Parallel reduction</li> <li>Matrix operations: BLAS-optimized matrix multiplication</li> </ul> <h4 id="cache-friendly-access" class="position-relative d-flex align-items-center group"> Cache-Friendly Access <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="cache-friendly-access" aria-haspopup="dialog" aria-label="Share link: Cache-Friendly Access"> Share link </button> </h4>Graph traversal optimized for CPU cache: <ul> <li>CSR format: Compressed Sparse Row for relationship storage</li> <li>Locality: Related nodes stored contiguously</li> <li>Prefetching: Predictive memory access</li> </ul> <h4 id="parallelization" class="position-relative d-flex align-items-center group"> Parallelization <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="parallelization" aria-haspopup="dialog" aria-label="Share link: Parallelization"> Share link </button> </h4>Algorithm execution parallelized across CPU cores: <ul> <li>PageRank: Parallel iteration with barrier synchronization</li> <li>Community detection: Parallel label updates</li> <li>Embeddings: Parallel random walk generation</li> </ul> Scaling: Near-linear speedup up to 8-16 cores (depending on graph density). <h3 id="operational-guidance" class="position-relative d-flex align-items-center group"> Operational Guidance <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="operational-guidance" aria-haspopup="dialog" aria-label="Share link: Operational Guidance"> Share link </button> </h3> <h4 id="when-to-run-algorithms" class="position-relative d-flex align-items-center group"> When to Run 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="when-to-run-algorithms" aria-haspopup="dialog" aria-label="Share link: When to Run Algorithms"> Share link </button> </h4>Offline (batch processing): <ul> <li>Large-scale community detection (millions of nodes)</li> <li>Full-graph PageRank computation</li> <li>Embedding generation for all nodes</li> </ul> Online (query-time): <ul> <li>Shortest path between specific nodes</li> <li>Local clustering coefficient</li> <li>k-hop neighborhood queries</li> </ul> Hybrid (materialized views): <ul> <li>Precompute PageRank, cache in node property</li> <li>Update periodically (e.g., daily) via batch job</li> <li>Query from cached property for fast access</li> </ul> Example: Materialized PageRank: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Batch job (run daily) CALL graph.pageRank('SocialNetwork', { relationship_type: 'KNOWS', iterations: 20 }) YIELD node, score WITH node, score MATCH (n:Person) WHERE n.id = node.id SET n.pagerank_score = score; -- Query uses cached property (fast) MATCH (p:Person) RETURN p.name, p.pagerank_score ORDER BY p.pagerank_score DESC LIMIT 10; </code></pre></div> <h4 id="resource-and-latency-caveats" class="position-relative d-flex align-items-center group"> Resource and Latency Caveats <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="resource-and-latency-caveats" aria-haspopup="dialog" aria-label="Share link: Resource and Latency Caveats"> Share link </button> </h4>Memory usage: <ul> <li>Embeddings: <code>num_nodes * dimensions * 4 bytes</code> (for float32) <ul> <li>Example: 1M nodes * 128 dims * 4B = 512 MB</li> </ul> </li> <li>Algorithm state: Varies (PageRank: ~2x node count)</li> </ul> Latency: <ul> <li>PageRank (1M nodes, 20 iterations): ~2-5 seconds</li> <li>Louvain (1M nodes): ~10-30 seconds</li> <li>Node2Vec (100K nodes, 10 walks): ~5-15 minutes</li> </ul> Tip: Use PROFILE to measure actual execution time before deploying to production. <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>From <code>REAL_TIME_ANALYTICS.md</code>: Combine graph algorithms with Change Data Capture (CDC) for real-time analytics. Architecture: <ol> <li>CDC stream: Capture graph changes (node/edge inserts/updates/deletes)</li> <li>Incremental update: Update algorithm state (e.g., incremental PageRank)</li> <li>Anomaly detection: Detect unusual patterns (e.g., sudden centrality spike)</li> <li>Webhook notification: Alert on anomalies</li> </ol> Example: Real-time fraud detection: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-yaml" data-lang="yaml"># cdc-config.yaml cdc: enabled: true webhooks: - url: "https://analytics.example.com/fraud-check" events: ["node.created", "edge.created"] filter: "label = 'Transaction'" </code></pre></div>Webhook payload: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-json" data-lang="json">{ "event": "node.created", "graph": "Payments", "node": { "id": 123456, "labels": ["Transaction"], "properties": { "amount": 10000, "from_account": "acct_001", "to_account": "acct_999" } }, "timestamp": "2024-01-15T14:30:00Z" } </code></pre></div>Analytics service: <ol> <li>Receives CDC event</li> <li>Queries graph for context (e.g., transaction history, account relationships)</li> <li>Computes anomaly score (e.g., transaction amount » avg, new relationship)</li> <li>Returns fraud probability</li> </ol> See also: <a href="/docs/use-cases/fraud-detection" >Real-Time Analytics</a> for complete workflow <h3 id="next-steps" class="position-relative d-flex align-items-center group"> Next Steps <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="next-steps" aria-haspopup="dialog" aria-label="Share link: Next Steps"> Share link </button> </h3><ul> <li><a href="/docs/model/data-model-and-types" >Data Model and Types</a> - Vector types and storage</li> <li><a href="/docs/query/indexing-and-optimization" >Indexing and Optimization</a> - HNSW vector indexes</li> <li><a href="/docs/use-cases/recommendations" >Use Case: Recommendations</a> - End-to-end recommendation system</li> <li><a href="/docs/use-cases/fraud-detection" >Use Case: Fraud Detection</a> - Anomaly detection with algorithms</li> <li><a href="/docs/analytics/graph-algorithms/" >Graph Algorithm Reference</a> - Complete algorithm catalog</li> </ul>