Graph Algorithms Tutorial | Geode Database

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closeModal(); } if(copyBtn && (e.target===copyBtn || (e.target.closest && e.target.closest('.hsm-copy')))) { e.preventDefault(); copyCurrent(); } }); document.addEventListener('keydown', e=>{ if(e.key==='Escape' && isOpen()) closeModal(); }); function trapFocus(){ if(trapBound) return; trapBound=true; modal.addEventListener('keydown', f=>{ if(f.key==='Tab' && isOpen()){ const focusable=[...modal.querySelectorAll('a[href],button,input,textarea,select,[tabindex]:not([tabindex="-1"])')].filter(el=>!el.hasAttribute('disabled')); if(!focusable.length) return; const first=focusable[0]; const last=focusable[focusable.length-1]; if(f.shiftKey && document.activeElement===first){ f.preventDefault(); last.focus(); } else if(!f.shiftKey && document.activeElement===last){ f.preventDefault(); first.focus(); } } }); } if(closeBtn) closeBtn.addEventListener('click', e=>{ e.preventDefault(); closeModal(); }); })(); </script>Learn to run powerful graph algorithms on your data in this hands-on 20-minute tutorial. <h3 id="prerequisites" class="position-relative d-flex align-items-center group"> Prerequisites <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="prerequisites" aria-haspopup="dialog" aria-label="Share link: Prerequisites"> Share link </button> </h3><ul> <li>Completed <a href="/docs/tutorials/match-basics/" >MATCH Basics Tutorial</a> </li> <li>Geode server running (<code>geode serve</code>)</li> <li>Access to Geode shell (<code>geode shell</code>)</li> <li>Understanding of basic graph concepts (nodes, relationships)</li> </ul> <h3 id="tutorial-overview" class="position-relative d-flex align-items-center group"> Tutorial Overview <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="tutorial-overview" aria-haspopup="dialog" aria-label="Share link: Tutorial Overview"> Share link </button> </h3>Time: 20 minutes Difficulty: Intermediate Topics: PageRank, shortest paths, community detection, centrality measures By the end of this tutorial, you’ll be able to: <ul> <li>Run PageRank to find influential nodes</li> <li>Find shortest paths between nodes</li> <li>Detect communities with Louvain algorithm</li> <li>Calculate centrality measures</li> <li>Apply algorithms to real-world problems</li> </ul> <h3 id="step-1-create-social-network" class="position-relative d-flex align-items-center group"> Step 1: Create Social Network <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="step-1-create-social-network" aria-haspopup="dialog" aria-label="Share link: Step 1: Create Social Network"> Share link </button> </h3>Create a realistic social network for algorithm demonstrations: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">CREATE GRAPH SocialNetwork; USE SocialNetwork; -- Create people CREATE (:Person {name: "Alice", id: 1}), (:Person {name: "Bob", id: 2}), (:Person {name: "Charlie", id: 3}), (:Person {name: "David", id: 4}), (:Person {name: "Emma", id: 5}), (:Person {name: "Frank", id: 6}), (:Person {name: "Grace", id: 7}), (:Person {name: "Henry", id: 8}); -- Create social connections MATCH (a:Person {name: "Alice"}), (b:Person {name: "Bob"}) CREATE (a)-[:KNOWS]->(b); MATCH (a:Person {name: "Alice"}), (c:Person {name: "Charlie"}) CREATE (a)-[:KNOWS]->(c); MATCH (b:Person {name: "Bob"}), (c:Person {name: "Charlie"}) CREATE (b)-[:KNOWS]->(c); MATCH (b:Person {name: "Bob"}), (d:Person {name: "David"}) CREATE (b)-[:KNOWS]->(d); MATCH (c:Person {name: "Charlie"}), (d:Person {name: "David"}) CREATE (c)-[:KNOWS]->(d); MATCH (d:Person {name: "David"}), (e:Person {name: "Emma"}) CREATE (d)-[:KNOWS]->(e); MATCH (e:Person {name: "Emma"}), (f:Person {name: "Frank"}) CREATE (e)-[:KNOWS]->(f); MATCH (e:Person {name: "Emma"}), (g:Person {name: "Grace"}) CREATE (e)-[:KNOWS]->(g); MATCH (f:Person {name: "Frank"}), (g:Person {name: "Grace"}) CREATE (f)-[:KNOWS]->(g); MATCH (g:Person {name: "Grace"}), (h:Person {name: "Henry"}) CREATE (g)-[:KNOWS]->(h); </code></pre></div>Expected output: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-fallback" data-lang="fallback">Created 8 nodes Created 10 relationships </code></pre></div> <h4 id="network-structure" class="position-relative d-flex align-items-center group"> Network Structure <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="network-structure" aria-haspopup="dialog" aria-label="Share link: Network Structure"> Share link </button> </h4>The network has two loosely connected communities: <ul> <li>Community 1: Alice, Bob, Charlie, David</li> <li>Community 2: Emma, Frank, Grace, Henry</li> <li>Bridge: David-Emma connection links the communities</li> </ul> <h4 id="what-you-learned" class="position-relative d-flex align-items-center group"> What You Learned <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="what-you-learned" aria-haspopup="dialog" aria-label="Share link: What You Learned"> Share link </button> </h4><ul> <li>Graph algorithms work on connected networks</li> <li>Community structure affects algorithm results</li> <li>Real networks often have multiple communities</li> </ul> <h3 id="step-2-pagerank---find-influential-nodes" class="position-relative d-flex align-items-center group"> Step 2: PageRank - Find Influential 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="step-2-pagerank---find-influential-nodes" aria-haspopup="dialog" aria-label="Share link: Step 2: PageRank - Find Influential Nodes"> Share link </button> </h3>Run PageRank to identify the most connected/influential people: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">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 ---------|-------- David | 0.185 Emma | 0.165 Bob | 0.142 Charlie | 0.138 Grace | 0.125 Frank | 0.095 Alice | 0.090 Henry | 0.060 </code></pre></div> <h4 id="understanding-pagerank" class="position-relative d-flex align-items-center group"> Understanding PageRank <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="understanding-pagerank" aria-haspopup="dialog" aria-label="Share link: Understanding PageRank"> Share link </button> </h4>Algorithm: Iteratively distributes influence through the network Score Meaning: <ul> <li>Higher score = more influential/central</li> <li>Score sums to 1.0 across all nodes</li> <li>Considers both direct and indirect connections</li> </ul> Parameters: <ul> <li><code>iterations</code>: Number of propagation rounds (default: 20)</li> <li><code>damping_factor</code>: Random jump probability (default: 0.85)</li> <li><code>relationship_type</code>: Which relationships to traverse</li> </ul> <h4 id="why-david-and-emma-score-highest" class="position-relative d-flex align-items-center group"> Why David and Emma Score Highest <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="why-david-and-emma-score-highest" aria-haspopup="dialog" aria-label="Share link: Why David and Emma Score Highest"> Share link </button> </h4><ul> <li>David: Bridge node connecting two communities (receives from both)</li> <li>Emma: High degree (3 connections) + central position</li> <li>Alice: Only 2 outgoing connections, peripheral position</li> <li>Henry: Dead-end node (only 1 connection)</li> </ul> <h4 id="what-you-learned-1" class="position-relative d-flex align-items-center group"> What You Learned <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="what-you-learned-1" aria-haspopup="dialog" aria-label="Share link: What You Learned"> Share link </button> </h4><ul> <li>PageRank identifies important nodes</li> <li>Bridge nodes score highly (connect communities)</li> <li>High degree ≠ always highest PageRank</li> <li>Position in network matters more than degree alone</li> </ul> <h3 id="step-3-shortest-path---find-connections" class="position-relative d-flex align-items-center group"> Step 3: Shortest Path - Find Connections <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="step-3-shortest-path---find-connections" aria-haspopup="dialog" aria-label="Share link: Step 3: Shortest Path - Find Connections"> Share link </button> </h3>Find the shortest path between two people: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">MATCH path = shortestPath( (a:Person {name: "Alice"})-[:KNOWS*]-(h:Person {name: "Henry"}) ) RETURN [n IN nodes(path) | n.name] AS path_names, 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_names | hops ------------------------------------------------|----- ["Alice", "Bob", "David", "Emma", "Grace", "Henry"] | 5 </code></pre></div> <h4 id="path-explanation" class="position-relative d-flex align-items-center group"> Path Explanation <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="path-explanation" aria-haspopup="dialog" aria-label="Share link: Path Explanation"> Share link </button> </h4>Alice → Bob → David → Emma → Grace → Henry <ul> <li>5 hops (relationships) to connect</li> <li>Shortest possible path through the network</li> <li>Goes through the David-Emma bridge</li> </ul> <h4 id="alternative-path-query" class="position-relative d-flex align-items-center group"> Alternative Path Query <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="alternative-path-query" aria-haspopup="dialog" aria-label="Share link: Alternative Path Query"> Share link </button> </h4>Find all shortest paths: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">MATCH path = allShortestPaths( (a:Person {name: "Alice"})-[:KNOWS*]-(h:Person {name: "Henry"}) ) RETURN [n IN nodes(path) | n.name] AS path_names, length(path) AS hops; </code></pre></div>May return multiple paths if there are ties. <h4 id="what-you-learned-2" class="position-relative d-flex align-items-center group"> What You Learned <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="what-you-learned-2" aria-haspopup="dialog" aria-label="Share link: What You Learned"> Share link </button> </h4><ul> <li><code>shortestPath()</code> finds minimal hop count</li> <li><code>*</code> indicates variable-length path</li> <li><code>nodes(path)</code> extracts nodes from path object</li> <li><code>length(path)</code> counts relationships (hops)</li> </ul> <h3 id="step-4-weighted-shortest-path-dijkstra" class="position-relative d-flex align-items-center group"> Step 4: Weighted Shortest Path (Dijkstra) <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="step-4-weighted-shortest-path-dijkstra" aria-haspopup="dialog" aria-label="Share link: Step 4: Weighted Shortest Path (Dijkstra)"> Share link </button> </h3>Add weights and find cheapest path: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Add interaction frequency weights MATCH (a:Person {name: "Alice"})-[r:KNOWS]->(b:Person {name: "Bob"}) SET r.frequency = 10; MATCH (a:Person {name: "Alice"})-[r:KNOWS]->(c:Person {name: "Charlie"}) SET r.frequency = 5; MATCH (b:Person {name: "Bob"})-[r:KNOWS]->(c:Person {name: "Charlie"}) SET r.frequency = 8; MATCH (b:Person {name: "Bob"})-[r:KNOWS]->(d:Person {name: "David"}) SET r.frequency = 3; MATCH (c:Person {name: "Charlie"})-[r:KNOWS]->(d:Person {name: "David"}) SET r.frequency = 7; -- Set remaining weights MATCH ()-[r:KNOWS]->() WHERE NOT EXISTS(r.frequency) SET r.frequency = 5; -- Find path with highest total frequency (strongest connections) CALL graph.dijkstra('SocialNetwork', { start_node: {name: "Alice"}, end_node: {name: "Henry"}, relationship_type: 'KNOWS', weight_property: 'frequency', minimize: false -- Maximize frequency }) YIELD path, cost RETURN [n IN nodes(path) | n.name] AS path_names, cost AS total_frequency; </code></pre></div>Expected output: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-fallback" data-lang="fallback">path_names | total_frequency ------------------------------------------------|---------------- ["Alice", "Bob", "Charlie", "David", "Emma", "Grace", "Henry"] | 38 </code></pre></div> <h4 id="weighted-vs-unweighted" class="position-relative d-flex align-items-center group"> Weighted vs Unweighted <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="weighted-vs-unweighted" aria-haspopup="dialog" aria-label="Share link: Weighted vs Unweighted"> Share link </button> </h4>Unweighted: Counts hops (5 hops Alice→Henry) Weighted: Considers relationship strength (38 total frequency) Different path may be optimal when weights are considered. <h4 id="what-you-learned-3" class="position-relative d-flex align-items-center group"> What You Learned <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="what-you-learned-3" aria-haspopup="dialog" aria-label="Share link: What You Learned"> Share link </button> </h4><ul> <li>Dijkstra’s algorithm finds weighted shortest paths</li> <li>Can minimize or maximize weights</li> <li>Useful for travel time, cost, strength, etc.</li> <li>Weights model real-world connection quality</li> </ul> <h3 id="step-5-community-detection-louvain" class="position-relative d-flex align-items-center group"> Step 5: Community Detection (Louvain) <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="step-5-community-detection-louvain" aria-haspopup="dialog" aria-label="Share link: Step 5: Community Detection (Louvain)"> Share link </button> </h3>Discover communities in the network: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">CALL graph.louvain('SocialNetwork', { relationship_type: 'KNOWS', max_iterations: 10 }) YIELD node, community RETURN community, collect(node.name) AS members, count(*) AS size ORDER BY size DESC; </code></pre></div>Expected output: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-fallback" data-lang="fallback">community | members | size ----------|-----------------------------------|----- 1 | ["David", "Emma", "Frank", "Grace", "Henry"] | 5 0 | ["Alice", "Bob", "Charlie"] | 3 </code></pre></div> <h4 id="community-detection-explained" class="position-relative d-flex align-items-center group"> Community Detection Explained <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-explained" aria-haspopup="dialog" aria-label="Share link: Community Detection Explained"> Share link </button> </h4>Louvain Algorithm: <ul> <li>Optimizes modularity (within-community vs between-community connections)</li> <li>Iteratively merges communities for better modularity</li> <li>Automatically determines number of communities</li> </ul> Interpretation: <ul> <li>Community 1: Larger, more interconnected group</li> <li>Community 0: Smaller, peripheral group</li> <li>David acts as bridge between communities</li> </ul> <h4 id="visualize-community-assignment" class="position-relative d-flex align-items-center group"> Visualize Community Assignment <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="visualize-community-assignment" aria-haspopup="dialog" aria-label="Share link: Visualize Community Assignment"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Persist community assignments CALL graph.louvain('SocialNetwork', { relationship_type: 'KNOWS' }) YIELD node, community WITH node, community MATCH (p:Person) WHERE p.id = node.id SET p.community = community; -- Query by community MATCH (p:Person) RETURN p.community, collect(p.name) AS members ORDER BY p.community; </code></pre></div> <h4 id="what-you-learned-4" class="position-relative d-flex align-items-center group"> What You Learned <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="what-you-learned-4" aria-haspopup="dialog" aria-label="Share link: What You Learned"> Share link </button> </h4><ul> <li>Louvain detects natural groupings</li> <li>No need to specify number of communities</li> <li>Community IDs are arbitrary (0, 1, 2, …)</li> <li>Useful for understanding network structure</li> </ul> <h3 id="step-6-betweenness-centrality" class="position-relative d-flex align-items-center group"> Step 6: 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="step-6-betweenness-centrality" aria-haspopup="dialog" aria-label="Share link: Step 6: Betweenness Centrality"> Share link </button> </h3>Find nodes that bridge communities: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">CALL graph.betweennessCentrality('SocialNetwork', { relationship_type: 'KNOWS', normalized: true }) YIELD node, score RETURN node.name AS person, score ORDER BY score DESC LIMIT 5; </code></pre></div>Expected output: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-fallback" data-lang="fallback">person | score --------|------- David | 0.428 Emma | 0.357 Bob | 0.214 Grace | 0.142 Charlie | 0.071 </code></pre></div> <h4 id="betweenness-centrality-explained" class="position-relative d-flex align-items-center group"> Betweenness Centrality Explained <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-explained" aria-haspopup="dialog" aria-label="Share link: Betweenness Centrality Explained"> Share link </button> </h4>Definition: Fraction of shortest paths passing through a node High Betweenness: <ul> <li>Node lies on many shortest paths</li> <li>Removing it would disconnect the network</li> <li>Bridge between communities</li> </ul> David’s High Score: <ul> <li>Only path between Alice-Emma passes through David</li> <li>Critical for information flow between communities</li> </ul> <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>How quickly can a node reach all others: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">CALL graph.closenessCentrality('SocialNetwork', { relationship_type: 'KNOWS', normalized: true }) YIELD node, score RETURN node.name AS person, score ORDER BY score DESC LIMIT 5; </code></pre></div>Expected output: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-fallback" data-lang="fallback">person | score --------|------- David | 0.636 Emma | 0.583 Bob | 0.538 Charlie | 0.538 Grace | 0.538 </code></pre></div>Interpretation: David can reach all nodes in fewest average hops. <h4 id="what-you-learned-5" class="position-relative d-flex align-items-center group"> What You Learned <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="what-you-learned-5" aria-haspopup="dialog" aria-label="Share link: What You Learned"> Share link </button> </h4><ul> <li>Betweenness: control over information flow</li> <li>Closeness: speed of reaching others</li> <li>Different centrality measures highlight different roles</li> <li>Critical for identifying key players</li> </ul> <h3 id="step-7-degree-centrality" class="position-relative d-flex align-items-center group"> Step 7: Degree Centrality <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="step-7-degree-centrality" aria-haspopup="dialog" aria-label="Share link: Step 7: Degree Centrality"> Share link </button> </h3>Simple but effective measure: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">MATCH (p:Person) OPTIONAL MATCH (p)-[r:KNOWS]-() RETURN p.name AS person, count(r) AS degree ORDER BY degree DESC; </code></pre></div>Expected output: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-fallback" data-lang="fallback">person | degree ---------|------- Emma | 3 David | 3 Bob | 3 Charlie | 3 Grace | 3 Frank | 2 Alice | 2 Henry | 1 </code></pre></div> <h4 id="degree-types" class="position-relative d-flex align-items-center group"> Degree Types <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-types" aria-haspopup="dialog" aria-label="Share link: Degree Types"> Share link </button> </h4>Total Degree: All connections (undirected) <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">count( (p)-[:KNOWS]-() ) </code></pre></div>Out-Degree: Outgoing only <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">count( (p)-[:KNOWS]->() ) </code></pre></div>In-Degree: Incoming only <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">count( (p)<-[:KNOWS]-() ) </code></pre></div> <h4 id="what-you-learned-6" class="position-relative d-flex align-items-center group"> What You Learned <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="what-you-learned-6" aria-haspopup="dialog" aria-label="Share link: What You Learned"> Share link </button> </h4><ul> <li>Degree = number of connections</li> <li>Simple but informative metric</li> <li>High degree ≠ high betweenness or closeness</li> <li>Useful baseline for comparison</li> </ul> <h3 id="step-8-triangle-counting" class="position-relative d-flex align-items-center group"> Step 8: Triangle Counting <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="step-8-triangle-counting" aria-haspopup="dialog" aria-label="Share link: Step 8: Triangle Counting"> Share link </button> </h3>Count triangles (three nodes all connected): <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">CALL graph.triangleCount('SocialNetwork', { relationship_type: 'KNOWS' }) YIELD node, count RETURN node.name AS person, count AS triangles ORDER BY count DESC; </code></pre></div>Expected output: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-fallback" data-lang="fallback">person | triangles ---------|---------- Bob | 2 Charlie | 2 David | 1 Emma | 1 Grace | 1 Frank | 1 Alice | 1 Henry | 0 </code></pre></div> <h4 id="understanding-triangles" class="position-relative d-flex align-items-center group"> Understanding Triangles <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="understanding-triangles" aria-haspopup="dialog" aria-label="Share link: Understanding Triangles"> Share link </button> </h4>Triangle: Three nodes A, B, C where A-B, B-C, and C-A all exist Examples in network: <ul> <li>Alice-Bob-Charlie: Triangle (all three connected)</li> <li>Bob-Charlie-David: Triangle</li> <li>Emma-Frank-Grace: Triangle</li> </ul> Significance: <ul> <li>Measure of clustering/cohesion</li> <li>High triangle count = tight-knit group</li> <li>Zero triangles = peripheral or bridging position</li> </ul> <h4 id="clustering-coefficient" class="position-relative d-flex align-items-center group"> Clustering Coefficient <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="clustering-coefficient" aria-haspopup="dialog" aria-label="Share link: Clustering Coefficient"> Share link </button> </h4>Related metric: fraction of possible triangles that exist <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">CALL graph.clusteringCoefficient('SocialNetwork', { relationship_type: 'KNOWS' }) YIELD node, coefficient RETURN node.name AS person, coefficient ORDER BY coefficient DESC; </code></pre></div> <h4 id="what-you-learned-7" class="position-relative d-flex align-items-center group"> What You Learned <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="what-you-learned-7" aria-haspopup="dialog" aria-label="Share link: What You Learned"> Share link </button> </h4><ul> <li>Triangles indicate cohesive groups</li> <li>Clustering coefficient measures local density</li> <li>High clustering = strongly connected neighborhood</li> <li>Useful for understanding local structure</li> </ul> <h3 id="step-9-connected-components" class="position-relative d-flex align-items-center group"> Step 9: 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="step-9-connected-components" aria-haspopup="dialog" aria-label="Share link: Step 9: Connected Components"> Share link </button> </h3>Find disconnected subgraphs: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">CALL graph.connectedComponents('SocialNetwork', { relationship_type: 'KNOWS' }) YIELD node, component RETURN component, collect(node.name) AS members, count(*) AS size ORDER BY size DESC; </code></pre></div>Expected output: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-fallback" data-lang="fallback">component | members | size ----------|--------------------------------------------------------|----- 0 | ["Alice", "Bob", "Charlie", "David", "Emma", "Frank", "Grace", "Henry"] | 8 </code></pre></div> <h4 id="interpretation" class="position-relative d-flex align-items-center group"> Interpretation <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="interpretation" aria-haspopup="dialog" aria-label="Share link: Interpretation"> Share link </button> </h4><ul> <li>One component: Entire network is connected</li> <li>Multiple components: Isolated subgraphs</li> </ul> <h4 id="test-with-disconnected-network" class="position-relative d-flex align-items-center group"> Test with Disconnected Network <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="test-with-disconnected-network" aria-haspopup="dialog" aria-label="Share link: Test with Disconnected Network"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Add isolated nodes CREATE (:Person {name: "Isolated1", id: 9}); CREATE (:Person {name: "Isolated2", id: 10}); CREATE (i1:Person {id: 9})-[:KNOWS]->(i2:Person {id: 10}); -- Re-run connected components CALL graph.connectedComponents('SocialNetwork', { relationship_type: 'KNOWS' }) YIELD node, component RETURN component, collect(node.name) AS members, count(*) AS size ORDER BY size DESC; </code></pre></div>Expected output: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-fallback" data-lang="fallback">component | members | size ----------|-----------------------------------|----- 0 | ["Alice", "Bob", ..., "Henry"] | 8 1 | ["Isolated1", "Isolated2"] | 2 </code></pre></div> <h4 id="what-you-learned-8" class="position-relative d-flex align-items-center group"> What You Learned <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="what-you-learned-8" aria-haspopup="dialog" aria-label="Share link: What You Learned"> Share link </button> </h4><ul> <li>Connected components find isolated subgraphs</li> <li>Useful for detecting network fragmentation</li> <li>Each component gets unique ID</li> <li>Can identify main network vs satellites</li> </ul> <h3 id="step-10-practical-application---recommendation-system" class="position-relative d-flex align-items-center group"> Step 10: Practical Application - 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="step-10-practical-application---recommendation-system" aria-haspopup="dialog" aria-label="Share link: Step 10: Practical Application - Recommendation System"> Share link </button> </h3>Use algorithms to build recommendations: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Find recommended friends for Alice -- (friends of friends, not already connected) MATCH (alice:Person {name: "Alice"})-[:KNOWS*2]-(fof:Person) WHERE NOT EXISTS((alice)-[:KNOWS]-(fof)) AND fof <> alice WITH fof, count(*) AS mutual_friends RETURN fof.name AS recommendation, mutual_friends ORDER BY mutual_friends DESC LIMIT 3; </code></pre></div>Expected output: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-fallback" data-lang="fallback">recommendation | mutual_friends ---------------|--------------- David | 2 </code></pre></div> <h4 id="enhanced-recommendations-with-pagerank" class="position-relative d-flex align-items-center group"> Enhanced Recommendations with PageRank <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="enhanced-recommendations-with-pagerank" aria-haspopup="dialog" aria-label="Share link: Enhanced Recommendations with PageRank"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Weight recommendations by influence CALL graph.pageRank('SocialNetwork', { relationship_type: 'KNOWS' }) YIELD node, score WITH node.id AS node_id, score MATCH (alice:Person {name: "Alice"})-[:KNOWS*2]-(fof:Person) WHERE NOT EXISTS((alice)-[:KNOWS]-(fof)) AND fof <> alice AND fof.id = node_id WITH fof, count(*) AS mutual_friends, score RETURN fof.name AS recommendation, mutual_friends, round(score * 1000) / 1000 AS influence_score ORDER BY mutual_friends DESC, influence_score DESC LIMIT 5; </code></pre></div> <h4 id="what-you-learned-9" class="position-relative d-flex align-items-center group"> What You Learned <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="what-you-learned-9" aria-haspopup="dialog" aria-label="Share link: What You Learned"> Share link </button> </h4><ul> <li>Graph algorithms power recommendation engines</li> <li>Combine multiple algorithms for better results</li> <li>Mutual friends + PageRank = weighted recommendations</li> <li>Real-world applications of graph analytics</li> </ul> <h3 id="complete-example-citation-network-analysis" class="position-relative d-flex align-items-center group"> Complete Example: Citation Network Analysis <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="complete-example-citation-network-analysis" aria-haspopup="dialog" aria-label="Share link: Complete Example: Citation Network Analysis"> Share link </button> </h3>Analyze academic paper citations: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">CREATE GRAPH CitationNetwork; USE CitationNetwork; -- Create papers CREATE (:Paper {title: "Graph Theory Basics", year: 2010, id: 1}), (:Paper {title: "Advanced Graph Algorithms", year: 2015, id: 2}), (:Paper {title: "Network Science", year: 2018, id: 3}), (:Paper {title: "Community Detection", year: 2020, id: 4}), (:Paper {title: "PageRank Survey", year: 2021, id: 5}); -- Create citations (older papers cited by newer) MATCH (old:Paper {id: 1}), (new:Paper {id: 2}) CREATE (new)-[:CITES]->(old); MATCH (old:Paper {id: 1}), (new:Paper {id: 3}) CREATE (new)-[:CITES]->(old); MATCH (old:Paper {id: 2}), (new:Paper {id: 3}) CREATE (new)-[:CITES]->(old); MATCH (old:Paper {id: 2}), (new:Paper {id: 4}) CREATE (new)-[:CITES]->(old); MATCH (old:Paper {id: 3}), (new:Paper {id: 4}) CREATE (new)-[:CITES]->(old); MATCH (old:Paper {id: 1}), (new:Paper {id: 5}) CREATE (new)-[:CITES]->(old); MATCH (old:Paper {id: 2}), (new:Paper {id: 5}) CREATE (new)-[:CITES]->(old); -- Find most influential papers (cited by many + cited by influential) CALL graph.pageRank('CitationNetwork', { relationship_type: 'CITES', iterations: 20 }) YIELD node, score RETURN node.title AS paper, node.year AS year, 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">paper | year | score -----------------------------|------|------- Graph Theory Basics | 2010 | 0.285 Advanced Graph Algorithms | 2015 | 0.238 Network Science | 2018 | 0.195 Community Detection | 2020 | 0.142 PageRank Survey | 2021 | 0.140 </code></pre></div>Insight: “Graph Theory Basics” (2010) is most influential (cited by many papers, including influential ones). <h4 id="what-you-learned-10" class="position-relative d-flex align-items-center group"> What You Learned <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="what-you-learned-10" aria-haspopup="dialog" aria-label="Share link: What You Learned"> Share link </button> </h4><ul> <li>PageRank models citation influence</li> <li>Older papers often have higher scores (more citations)</li> <li>Algorithms reveal hidden patterns</li> <li>Domain-specific interpretations matter</li> </ul> <h3 id="algorithm-selection-guide" class="position-relative d-flex align-items-center group"> Algorithm Selection Guide <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="algorithm-selection-guide" aria-haspopup="dialog" aria-label="Share link: Algorithm Selection Guide"> Share link </button> </h3> <h4 id="choose-pagerank-when" class="position-relative d-flex align-items-center group"> Choose PageRank when: <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="choose-pagerank-when" aria-haspopup="dialog" aria-label="Share link: Choose PageRank when:"> Share link </button> </h4><ul> <li>Finding influential/important nodes</li> <li>Ranking nodes by connectivity</li> <li>Building recommendation systems</li> <li>Citation analysis, web page ranking</li> </ul> <h4 id="choose-shortest-path-when" class="position-relative d-flex align-items-center group"> Choose Shortest Path when: <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="choose-shortest-path-when" aria-haspopup="dialog" aria-label="Share link: Choose Shortest Path when:"> Share link </button> </h4><ul> <li>Finding connections between nodes</li> <li>Route planning, navigation</li> <li>Understanding network distances</li> <li>Six degrees of separation analysis</li> </ul> <h4 id="choose-community-detection-when" class="position-relative d-flex align-items-center group"> Choose Community Detection when: <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="choose-community-detection-when" aria-haspopup="dialog" aria-label="Share link: Choose Community Detection when:"> Share link </button> </h4><ul> <li>Discovering natural groupings</li> <li>Understanding network structure</li> <li>Market segmentation</li> <li>Fraud ring detection</li> </ul> <h4 id="choose-centrality-measures-when" class="position-relative d-flex align-items-center group"> Choose Centrality Measures when: <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="choose-centrality-measures-when" aria-haspopup="dialog" aria-label="Share link: Choose Centrality Measures when:"> Share link </button> </h4><ul> <li>Identifying key players</li> <li>Finding bottlenecks (betweenness)</li> <li>Measuring reachability (closeness)</li> <li>Detecting influencers (degree)</li> </ul> <h4 id="choose-triangle-counting-when" class="position-relative d-flex align-items-center group"> Choose Triangle Counting when: <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="choose-triangle-counting-when" aria-haspopup="dialog" aria-label="Share link: Choose Triangle Counting when:"> Share link </button> </h4><ul> <li>Measuring cohesion</li> <li>Detecting tightly-knit groups</li> <li>Understanding local clustering</li> <li>Spam/fake account detection</li> </ul> <h3 id="performance-tips" class="position-relative d-flex align-items-center group"> Performance Tips <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-tips" aria-haspopup="dialog" aria-label="Share link: Performance Tips"> Share link </button> </h3> <h4 id="for-large-graphs-millions-of-nodes" class="position-relative d-flex align-items-center group"> For Large Graphs (millions of 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="for-large-graphs-millions-of-nodes" aria-haspopup="dialog" aria-label="Share link: For Large Graphs (millions of nodes):"> Share link </button> </h4><ol> <li> Use relationship type filters: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">{relationship_type: 'KNOWS'} -- Faster than processing all types </code></pre></div></li> <li> Limit iterations: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">{iterations: 10} -- Fewer iterations = faster (may sacrifice accuracy) </code></pre></div></li> <li> Sample large graphs: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Work on subgraph first MATCH (n:Person) WHERE rand() < 0.1 -- 10% sample ... </code></pre></div></li> <li> Create indexes: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">CREATE INDEX person_id_idx ON Person(id) USING hash; </code></pre></div></li> <li> Persist results: <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Store PageRank scores for reuse CALL graph.pageRank(...) YIELD node, score WITH node, score MATCH (p:Person) WHERE p.id = node.id SET p.pagerank = score; </code></pre></div></li> </ol> <h3 id="practice-exercises" class="position-relative d-flex align-items-center group"> Practice Exercises <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="practice-exercises" aria-haspopup="dialog" aria-label="Share link: Practice Exercises"> Share link </button> </h3> <h4 id="exercise-1-influence-analysis" class="position-relative d-flex align-items-center group"> Exercise 1: Influence Analysis <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="exercise-1-influence-analysis" aria-haspopup="dialog" aria-label="Share link: Exercise 1: Influence Analysis"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Calculate multiple centrality measures for each person -- Combine PageRank, degree, betweenness, and closeness -- Find person who ranks highest across all measures </code></pre></div> <h4 id="exercise-2-community-comparison" class="position-relative d-flex align-items-center group"> Exercise 2: Community Comparison <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="exercise-2-community-comparison" aria-haspopup="dialog" aria-label="Share link: Exercise 2: Community Comparison"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Run Louvain community detection -- For each community, calculate: -- - Average PageRank -- - Average degree -- - Number of triangles -- Which community is most cohesive? </code></pre></div> <h4 id="exercise-3-path-analysis" class="position-relative d-flex align-items-center group"> Exercise 3: Path Analysis <button type="button" class="h-share btn btn-link p-0 text-decoration-none link-secondary opacity-50 hover-opacity-100 transition-all ms-1" data-share-target="exercise-3-path-analysis" aria-haspopup="dialog" aria-label="Share link: Exercise 3: Path Analysis"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Find all paths between Alice and Henry -- Filter paths by length (3-5 hops) -- Calculate total frequency (sum of relationship weights) -- Return top 3 paths by frequency </code></pre></div> <h3 id="solutions" class="position-relative d-flex align-items-center group"> Solutions <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="solutions" aria-haspopup="dialog" aria-label="Share link: Solutions"> Share link </button> </h3><details> <summary>Exercise 1 Solution</summary> <div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- Get PageRank CALL graph.pageRank('SocialNetwork', {relationship_type: 'KNOWS'}) YIELD node, score WITH node.id AS id, score AS pr -- Get degree MATCH (p:Person) WHERE p.id = id OPTIONAL MATCH (p)-[r:KNOWS]-() WITH p, pr, count(r) AS degree -- Get betweenness CALL graph.betweennessCentrality('SocialNetwork', {relationship_type: 'KNOWS'}) YIELD node, score WHERE node.id = p.id WITH p, pr, degree, score AS between -- Get closeness CALL graph.closenessCentrality('SocialNetwork', {relationship_type: 'KNOWS'}) YIELD node, score WHERE node.id = p.id -- Normalize and rank RETURN p.name, pr, degree, between, score AS closeness, (pr + degree/10.0 + between + score) / 4 AS avg_rank ORDER BY avg_rank DESC; </code></pre></div></details> <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>Continue your graph analytics journey: <ol> <li><a href="/docs/tutorials/vector-search-tutorial/" >Vector Search Tutorial</a> - ML embeddings and similarity search</li> <li><a href="/docs/analytics/graph-algorithms/" >Graph Algorithms Guide</a> - Complete algorithm catalog</li> <li><a href="/docs/performance/" >Performance Tuning</a> - Optimize algorithm execution</li> <li><a href="/docs/use-cases/overview/" >Use Case Guides</a> - Domain-specific applications</li> </ol> <h3 id="quick-reference" class="position-relative d-flex align-items-center group"> Quick Reference <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="quick-reference" aria-haspopup="dialog" aria-label="Share link: Quick Reference"> Share link </button> </h3> <h4 id="algorithm-calls" class="position-relative d-flex align-items-center group"> Algorithm Calls <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-calls" aria-haspopup="dialog" aria-label="Share link: Algorithm Calls"> Share link </button> </h4><div class="highlight"><pre tabindex="0" class="chroma"><code class="language-gql" data-lang="gql">-- PageRank CALL graph.pageRank(graph_name, {relationship_type, iterations, damping_factor}) YIELD node, score -- Shortest Path MATCH path = shortestPath((a)-[:TYPE*]-(b)) -- Dijkstra (weighted) CALL graph.dijkstra(graph_name, {start_node, end_node, weight_property}) YIELD path, cost -- Community Detection CALL graph.louvain(graph_name, {relationship_type, max_iterations}) YIELD node, community -- Betweenness Centrality CALL graph.betweennessCentrality(graph_name, {relationship_type, normalized}) YIELD node, score -- Closeness Centrality CALL graph.closenessCentrality(graph_name, {relationship_type, normalized}) YIELD node, score -- Triangle Counting CALL graph.triangleCount(graph_name, {relationship_type}) YIELD node, count -- Connected Components CALL graph.connectedComponents(graph_name, {relationship_type}) YIELD node, component </code></pre></div><hr> Tutorial Complete! You now understand graph algorithms and their applications in Geode. Next: <a href="/docs/tutorials/vector-search-tutorial/" >Vector Search Tutorial</a>