@graphty/algorithms

A comprehensive TypeScript graph algorithms library with 98 algorithms optimized for browser environments and visualization applications.

Features

• TypeScript-first: Full type safety with comprehensive type definitions
• Browser-optimized: Designed to run efficiently in web browsers
• Modular: Import only the algorithms you need
• Comprehensive: 98 graph algorithms including traversal, shortest paths, centrality, clustering, flow, matching, link prediction, and more
• Interactive Examples: Live demos with visualizations for all algorithms
• Performance Analysis: Detailed benchmarks comparing algorithm performance
• Well-tested: Extensive test suite with high coverage
• Standards-compliant: Follows conventional commits and semantic versioning

Performance Optimizations

The library automatically optimizes performance for large graphs (≥10,000 nodes) using:

• Direction-Optimized BFS: Dynamically switches between top-down and bottom-up search strategies, providing up to 42x speedup on large graphs
• CSR Graph Format: Compressed Sparse Row format for cache-efficient memory access
• Bit-Packed Data Structures: 8x memory reduction using bit arrays for boolean data

These optimizations are applied automatically - no configuration needed! Just use the standard API:

// Automatically uses optimized implementation for large graphs
const result = breadthFirstSearch(largeGraph, startNode);

All BFS-based algorithms benefit from these optimizations:

• breadthFirstSearch, shortestPathBFS, singleSourceShortestPathBFS
• betweennessCentrality, closenessCentrality
• Connected component algorithms

Performance Benchmarks

| Graph Size | Standard BFS | Optimized BFS | Speedup | | ---------- | ------------ | ------------- | ------- | | 10K nodes | 4.40ms | 6.34ms | 0.69x | | 50K nodes | 158.64ms | 44.27ms | 3.58x | | 100K nodes | 5,370ms | 126ms | 42.58x |

Note: Optimizations activate automatically for graphs ≥10K nodes to avoid conversion overhead on smaller graphs.

Learn More

• 📖 Performance Guide - Detailed optimization explanations
• 🔄 Migration Guide - Upgrading from older versions
• 💾 Memory vs Speed Tradeoffs - Making the right choices

Installation

npm install @graphty/algorithms

Quick Start

import { Graph, breadthFirstSearch, dijkstra } from "@graphty/algorithms";

// Create a new graph
const graph = new Graph();

// Add nodes and edges
graph.addNode("A");
graph.addNode("B");
graph.addNode("C");
graph.addEdge("A", "B", 1); // source, target, weight
graph.addEdge("B", "C", 2);

// Basic graph operations
console.log(graph.nodeCount); // 3
console.log(graph.totalEdgeCount); // 2
console.log(graph.hasEdge("A", "B")); // true

// Run algorithms
const traversal = breadthFirstSearch(graph, "A");
console.log(traversal.order); // ['A', 'B', 'C']

const shortestPaths = dijkstra(graph, "A");
// Get distance to C
const pathToC = shortestPaths.get("C");
console.log(pathToC?.distance); // 3

API Reference

Graph Class

The core data structure for representing graphs.

class Graph {
    constructor(config?: Partial<GraphConfig>);
}

Configuration Options

interface GraphConfig {
    directed: boolean; // Default: false
    allowSelfLoops: boolean; // Default: false
    allowParallelEdges: boolean; // Default: false
}

Node Operations

// Add a node with optional data
graph.addNode(id: NodeId, data?: Record<string, unknown>): void

// Remove a node and all its edges
graph.removeNode(id: NodeId): boolean

// Check if a node exists
graph.hasNode(id: NodeId): boolean

// Get node details
graph.getNode(id: NodeId): Node | undefined

// Get all nodes
graph.nodes(): IterableIterator<Node>

Edge Operations

// Add an edge with optional weight and data
graph.addEdge(
  source: NodeId,
  target: NodeId,
  weight?: number,
  data?: Record<string, unknown>
): void

// Remove an edge
graph.removeEdge(source: NodeId, target: NodeId): boolean

// Check if an edge exists
graph.hasEdge(source: NodeId, target: NodeId): boolean

// Get edge details
graph.getEdge(source: NodeId, target: NodeId): Edge | undefined

// Get all edges
graph.edges(): IterableIterator<Edge>

Graph Properties

// Number of nodes
graph.nodeCount: number

// Total number of edges (counts both directions for undirected)
graph.totalEdgeCount: number

// Number of unique edges
graph.uniqueEdgeCount: number

// Check if graph is directed
graph.isDirected: boolean

Degree Operations

// Total degree (in + out for directed)
graph.degree(nodeId: NodeId): number

// In-degree (directed graphs only)
graph.inDegree(nodeId: NodeId): number

// Out-degree
graph.outDegree(nodeId: NodeId): number

Neighbor Operations

// Get neighboring nodes
graph.neighbors(nodeId: NodeId): IterableIterator<NodeId>

// Get incoming neighbors (directed graphs)
graph.inNeighbors(nodeId: NodeId): IterableIterator<NodeId>

// Get outgoing neighbors
graph.outNeighbors(nodeId: NodeId): IterableIterator<NodeId>

Utility Methods

// Create a deep copy
graph.clone(): Graph

// Clear all nodes and edges
graph.clear(): void

// Get a copy of the graph configuration
graph.getConfig(): GraphConfig

Traversal Algorithms

Breadth-First Search (BFS)

import { breadthFirstSearch, shortestPathBFS, singleSourceShortestPathBFS, isBipartite } from '@graphty/algorithms';

// Basic BFS traversal
const result = breadthFirstSearch(graph, startNode, {
  targetNode?: NodeId,     // Optional: stop when target is reached
  visitCallback?: (node: NodeId, level: number) => void
});
// Returns: TraversalResult { visited: Set<NodeId>, order: NodeId[], tree?: Map<NodeId, NodeId | null> }

// Note: For graphs with ≥10K nodes, BFS automatically uses:
// - Direction-Optimized BFS (switches between top-down/bottom-up)
// - CSR graph format for cache efficiency
// - Bit-packed data structures for memory efficiency

// Find shortest path between two nodes (unweighted)
const path = shortestPathBFS(graph, source, target);
// Returns: ShortestPathResult | null
// ShortestPathResult = { distance: number, path: NodeId[], predecessor: Map<NodeId, NodeId | null> }

// Find all shortest paths from a source
const paths = singleSourceShortestPathBFS(graph, source);
// Returns: Map<NodeId, ShortestPathResult>

// Check if graph is bipartite
const bipartite = isBipartite(graph);
// Returns: { isBipartite: boolean, coloring?: Map<NodeId, number> }

Depth-First Search (DFS)

import { depthFirstSearch, topologicalSort, hasCycleDFS, findStronglyConnectedComponents } from '@graphty/algorithms';

// Basic DFS traversal
const result = depthFirstSearch(graph, startNode, {
  targetNode?: NodeId,      // Optional: stop when target is reached
  visitCallback?: (node: NodeId, level: number) => void,
  recursive?: boolean,      // Use recursive implementation (default: false)
  preOrder?: boolean        // Visit nodes in pre-order (default: true)
});
// Returns: TraversalResult

// Topological sort (for DAGs)
const sorted = topologicalSort(graph);
// Returns: NodeId[] | null (null if cycle detected)

// Cycle detection
const hasCycle = hasCycleDFS(graph);
// Returns: boolean

// Find strongly connected components using DFS
const sccs = findStronglyConnectedComponents(graph);
// Returns: NodeId[][]

Shortest Path Algorithms

Dijkstra's Algorithm

import {
  dijkstra,
  dijkstraPath,
  singleSourceShortestPath,
  allPairsShortestPath
} from '@graphty/algorithms'

// Single-source shortest paths
const result = dijkstra(graph, source, {
  target?: NodeId // Optional: stop when target is reached
})
// Returns: Map<NodeId, ShortestPathResult>
// ShortestPathResult = { distance: number, path: NodeId[], predecessor: Map<NodeId, NodeId | null> }

// Get specific path
const path = dijkstraPath(graph, source, target)
// Returns: ShortestPathResult | null

// All shortest paths from source
const paths = singleSourceShortestPath(graph, source)
// Returns: Map<NodeId, ShortestPathResult>

// All pairs shortest paths
const allPairs = allPairsShortestPath(graph)
// Returns: Map<NodeId, Map<NodeId, ShortestPathResult>>

Bellman-Ford Algorithm

import { bellmanFord, bellmanFordPath, hasNegativeCycle } from "@graphty/algorithms";

// Single-source shortest paths (handles negative weights)
const result = bellmanFord(graph, source);
// Returns: BellmanFordResult {
//   distances: Map<NodeId, number>,
//   predecessors: Map<NodeId, NodeId | null>,
//   hasNegativeCycle: boolean,
//   negativeCycleNodes?: Set<NodeId>
// }

// Get specific path
const path = bellmanFordPath(graph, source, target);
// Returns: ShortestPathResult | null

// Check for negative cycles
const result = hasNegativeCycle(graph);
// Returns: BellmanFordResult with hasNegativeCycle boolean

Floyd-Warshall Algorithm

import { floydWarshall, floydWarshallPath, transitiveClosure } from "@graphty/algorithms";

// All pairs shortest paths
const result = floydWarshall(graph);
// Returns: { distances: Map<NodeId, Map<NodeId, number>>, next: Map<NodeId, Map<NodeId, NodeId | null>> }

// Get specific path between any pair
const path = floydWarshallPath(result, source, target);
// Returns: NodeId[] | null

// Compute transitive closure
const closure = transitiveClosure(graph);
// Returns: Map<NodeId, Set<NodeId>>

Centrality Algorithms

Degree Centrality

import { degreeCentrality, nodeDegreeCentrality } from "@graphty/algorithms";

// Calculate for all nodes
const centralities = degreeCentrality(graph, {
    normalized: boolean, // Default: false
    weight: string, // Optional: edge property for weighted degree
});
// Returns: CentralityResult (Record<string, number>)

// Calculate for single node
const centrality = nodeDegreeCentrality(graph, nodeId, { normalized: boolean });
// Returns: number

Betweenness Centrality

import { betweennessCentrality, nodeBetweennessCentrality, edgeBetweennessCentrality } from "@graphty/algorithms";

// Node betweenness for all nodes
const centralities = betweennessCentrality(graph, {
    normalized: boolean, // Default: false
    weight: string, // Optional: use weighted shortest paths
    endpoints: boolean, // Default: false, include endpoints in paths
});
// Returns: CentralityResult (Record<string, number>)

// Single node betweenness
const centrality = nodeBetweennessCentrality(graph, nodeId, options);
// Returns: number

// Edge betweenness
const edgeCentralities = edgeBetweennessCentrality(graph, options);
// Returns: Map<string, number> (edge ID to centrality)

Closeness Centrality

import { closenessCentrality, nodeClosenessCentrality, weightedClosenessCentrality } from "@graphty/algorithms";

// Closeness for all nodes
const centralities = closenessCentrality(graph, {
    normalized: boolean, // Default: false
});
// Returns: CentralityResult (Record<string, number>)

// Single node closeness
const centrality = nodeClosenessCentrality(graph, nodeId, {
    normalized: boolean,
});
// Returns: number

// Weighted closeness
const centralities = weightedClosenessCentrality(graph, {
    normalized: boolean,
    weight: string, // Edge property for weights
});
// Returns: CentralityResult (Record<string, number>)

// Single node weighted closeness
const centrality = nodeWeightedClosenessCentrality(graph, nodeId, {
    normalized: boolean,
    weight: string, // Edge property for weights
});
// Returns: number

PageRank

import { pageRank, personalizedPageRank, topPageRankNodes } from "@graphty/algorithms";

// Standard PageRank
const result = pageRank(graph, {
    dampingFactor: number, // Default: 0.85
    maxIterations: number, // Default: 100
    tolerance: number, // Default: 1e-6
    initialRanks: Record<string, number>,
    personalization: Record<string, number>,
});
// Returns: { ranks: Record<string, number>, iterations: number, converged: boolean }

// Personalized PageRank (with bias)
const ranks = personalizedPageRank(graph, personalization, options);
// personalization: Map<NodeId, number> - restart probabilities
// Returns: CentralityResult (Record<string, number>)

// Get top N nodes by PageRank
const topNodes = topPageRankNodes(graph, n, options);
// Returns: Array<{ node: NodeId, rank: number }>

// Alternative PageRank that returns CentralityResult format
const centralities = pageRankCentrality(graph, options);
// Returns: CentralityResult (Record<string, number>)

Eigenvector Centrality

import { eigenvectorCentrality, nodeEigenvectorCentrality } from "@graphty/algorithms";

// Calculate eigenvector centrality for all nodes
const centralities = eigenvectorCentrality(graph, {
    maxIterations: number, // Default: 100
    tolerance: number, // Default: 1e-6
});
// Returns: CentralityResult (Record<string, number>)

// Single node eigenvector centrality
const centrality = nodeEigenvectorCentrality(graph, nodeId, options);
// Returns: number

Katz Centrality

import { katzCentrality, nodeKatzCentrality } from "@graphty/algorithms";

// Calculate Katz centrality for all nodes
const centralities = katzCentrality(graph, {
    alpha: number, // Attenuation factor (default: 0.1)
    beta: number, // Weight for direct connections (default: 1.0)
    maxIterations: number, // Default: 100
    tolerance: number, // Default: 1e-6
    normalized: boolean, // Default: true
});
// Returns: CentralityResult (Record<string, number>)

// Single node Katz centrality
const centrality = nodeKatzCentrality(graph, nodeId, options);
// Returns: number

HITS Algorithm

import { hits, nodeHITS } from "@graphty/algorithms";

// Calculate hub and authority scores
const result = hits(graph, {
    maxIterations: number, // Default: 100
    tolerance: number, // Default: 1e-6
});
// Returns: HITSResult { hubs: CentralityResult, authorities: CentralityResult }

// Single node HITS scores
const scores = nodeHITS(graph, nodeId, options);
// Returns: { hub: number, authority: number }

Connected Components

Basic Component Operations

import {
    connectedComponents,
    isConnected,
    numberOfConnectedComponents,
    largestConnectedComponent,
    getConnectedComponent,
} from "@graphty/algorithms";

// Find all components
const components = connectedComponents(graph);
// Returns: NodeId[][] (array of component arrays)

// Check if graph is connected
const connected = isConnected(graph);
// Returns: boolean

// Count components
const count = numberOfConnectedComponents(graph);
// Returns: number

// Get largest component
const largest = largestConnectedComponent(graph);
// Returns: NodeId[]

// Get component containing a specific node
const component = getConnectedComponent(graph, nodeId);
// Returns: Set<NodeId>

Strongly Connected Components

import {
    stronglyConnectedComponents,
    findStronglyConnectedComponents,
    isStronglyConnected,
    condensationGraph,
} from "@graphty/algorithms";

// Find SCCs using Tarjan's algorithm
const sccs = stronglyConnectedComponents(graph);
// Returns: ComponentResult

// Alternative: using DFS
const sccs = findStronglyConnectedComponents(graph);
// Returns: NodeId[][]

// Check if directed graph is strongly connected
const stronglyConnected = isStronglyConnected(graph);
// Returns: boolean

// Create condensation graph (DAG of SCCs)
const condensation = condensationGraph(graph);
// Returns: { graph: Graph, componentMap: Map<NodeId, number> }

// Alternative DFS-based connected components
const components = connectedComponentsDFS(graph);
// Returns: ComponentResult

Weakly Connected Components

import { weaklyConnectedComponents, isWeaklyConnected } from "@graphty/algorithms";

// Find WCCs (ignoring edge direction)
const wccs = weaklyConnectedComponents(graph);
// Returns: ComponentResult

// Check if directed graph is weakly connected
const weaklyConnected = isWeaklyConnected(graph);
// Returns: boolean

Data Structures

Priority Queue

Min-heap implementation used internally by algorithms.

import { PriorityQueue } from "@graphty/algorithms";

const pq = new PriorityQueue<T>((a, b) => a.priority - b.priority);

pq.enqueue(item);
pq.dequeue();
pq.peek();
pq.isEmpty();
pq.size;
pq.clear();

Union-Find (Disjoint Set)

Efficient data structure for tracking connected components.

import { UnionFind } from "@graphty/algorithms";

const uf = new UnionFind<T>();

uf.makeSet(item);
uf.find(item);
uf.union(item1, item2);
uf.connected(item1, item2);
uf.getSetSize(item);
uf.numberOfSets;

Minimum Spanning Tree Algorithms

Kruskal's Algorithm

import { kruskalMST, minimumSpanningTree } from "@graphty/algorithms";

// Find MST using Kruskal's algorithm
const mst = kruskalMST(graph);
// Returns: { edges: Edge[], weight: number }

// Alternative alias
const mst = minimumSpanningTree(graph);

Prim's Algorithm

import { primMST } from '@graphty/algorithms';

// Find MST using Prim's algorithm
const mst = primMST(graph, startNode?);
// Returns: { edges: Edge[], weight: number }

Community Detection Algorithms

Louvain Method

import { louvain } from "@graphty/algorithms";

// Detect communities using Louvain method
const communities = louvain(graph, {
    resolution: number, // Default: 1.0
    randomSeed: number,
});
// Returns: { communities: Map<NodeId, number>, modularity: number }

Leiden Algorithm

import { leiden } from "@graphty/algorithms";

// Improved community detection
const communities = leiden(graph, {
    resolution: number, // Default: 1.0
    iterations: number, // Default: 10
    randomSeed: number,
});
// Returns: { communities: Map<NodeId, number>, modularity: number }

Label Propagation

import { labelPropagation, labelPropagationAsync, labelPropagationSemiSupervised } from "@graphty/algorithms";

// Basic label propagation
const labels = labelPropagation(graph, {
    maxIterations: number, // Default: 100
});
// Returns: Map<NodeId, number>

// Asynchronous version
const labels = labelPropagationAsync(graph, options);

// Semi-supervised with seed communities
const labels = labelPropagationSemiSupervised(graph, seedLabels, options);

Girvan-Newman Algorithm

import { girvanNewman } from "@graphty/algorithms";

// Edge betweenness based community detection
const dendrogram = girvanNewman(graph, {
    targetCommunities: number, // Stop at this many communities
});
// Returns: { levels: Array<{ modularity: number, communities: NodeId[][] }> }

Pathfinding Algorithms

A* Algorithm

import { astar } from "@graphty/algorithms";

// A* pathfinding with heuristic
const path = astar(
    graph, // Map<T, Map<T, number>> adjacency list
    start,
    goal,
    heuristic, // (node: T, goal: T) => number
);
// Returns: { path: T[], cost: number } | null

Flow Algorithms

Maximum Flow

import { fordFulkerson, edmondsKarp } from '@graphty/algorithms';

// Ford-Fulkerson using DFS
const flow = fordFulkerson(graph, source, sink, {
  capacityKey?: string      // Edge property for capacity
});
// Returns: { maxFlow: number, flowGraph: Map<NodeId, Map<NodeId, number>> }

// Edmonds-Karp using BFS (better complexity)
const flow = edmondsKarp(graph, source, sink, options);

// Create bipartite flow network
const flowNetwork = createBipartiteFlowNetwork(leftNodes, rightNodes, edges, capacities?);
// Returns: FlowNetwork

Minimum Cut

import { minSTCut, stoerWagner, kargerMinCut } from '@graphty/algorithms';

// Min s-t cut using max flow
const cut = minSTCut(graph, source, sink);
// Returns: { cutValue: number, sourcePartition: Set<NodeId>, sinkPartition: Set<NodeId> }

// Global minimum cut (Stoer-Wagner)
const cut = stoerWagner(graph);
// Returns: { cutValue: number, partition1: Set<NodeId>, partition2: Set<NodeId> }

// Randomized min cut (Karger)
const cut = kargerMinCut(graph, iterations?);
// Returns: { cutValue: number, partition1: Set<NodeId>, partition2: Set<NodeId> }

Clustering Algorithms

Hierarchical Clustering

import { hierarchicalClustering, cutDendrogram, cutDendrogramKClusters } from "@graphty/algorithms";

// Agglomerative clustering
const result = hierarchicalClustering(graph, linkage);
// graph: Map<NodeId, Set<NodeId>>
// linkage: 'single' | 'complete' | 'average' | 'ward' (default: 'single')
// Returns: HierarchicalClusteringResult { root: ClusterNode, dendrogram: ClusterNode[], clusters: Map<number, Set<NodeId>[]> }

// Cut at specific height
const clusters = cutDendrogram(result.root, height);
// Returns: Set<NodeId>[]

// Get exactly k clusters
const clusters = cutDendrogramKClusters(result.root, k);
// Returns: Set<NodeId>[]

K-Core Decomposition

import { kCoreDecomposition, getKCore, kTruss, degeneracyOrdering } from "@graphty/algorithms";

// Find all k-cores
const result = kCoreDecomposition(graph);
// graph: Map<NodeId, Set<NodeId>>
// Returns: KCoreResult { cores: Map<number, Set<NodeId>>, coreness: Map<NodeId, number>, maxCore: number }

// Extract specific k-core subgraph
const kCore = getKCore(graph, k);
// Returns: Set<NodeId>

// Find k-truss (triangular cores)
const truss = kTruss(graph, k);
// Returns: Set<string> (edge strings)

// Degeneracy ordering
const ordering = degeneracyOrdering(graph);
// Returns: NodeId[]

Spectral Clustering

import { spectralClustering } from "@graphty/algorithms";

// Spectral clustering using graph Laplacian
const result = spectralClustering(graph, {
    k: number, // Number of clusters
    laplacianType: "unnormalized" | "normalized" | "randomWalk", // Default: 'normalized'
    maxIterations: number, // Default: 100
    tolerance: number, // Default: 1e-4
});
// Returns: SpectralClusteringResult { communities: NodeId[][], clusterAssignments: Map<NodeId, number> }

Markov Clustering (MCL)

import { markovClustering, calculateMCLModularity } from "@graphty/algorithms";

// MCL algorithm for network clustering
const result = markovClustering(graph, {
    expansion: number, // Expansion parameter (default: 2)
    inflation: number, // Inflation parameter (default: 2)
    maxIterations: number, // Default: 100
    tolerance: number, // Default: 1e-6
});
// Returns: MCLResult { communities: NodeId[][], attractors: Set<NodeId>, iterations: number, converged: boolean }

// Calculate modularity of MCL clustering result
const modularity = calculateMCLModularity(graph, result.communities);
// Returns: number

Matching Algorithms

Bipartite Matching

import { maximumBipartiteMatching, greedyBipartiteMatching, bipartitePartition } from "@graphty/algorithms";

// Maximum bipartite matching (Hungarian algorithm)
const matching = maximumBipartiteMatching(graph, {
    leftNodes: Set<NodeId>, // Optional: specify left partition
    rightNodes: Set<NodeId>, // Optional: specify right partition
});
// Returns: BipartiteMatchingResult { matching: Map<NodeId, NodeId>, size: number }

// Greedy bipartite matching (faster, approximate)
const matching = greedyBipartiteMatching(graph, options);

// Partition graph into bipartite sets
const partition = bipartitePartition(graph);
// Returns: { left: Set<NodeId>, right: Set<NodeId> } | null

Graph Isomorphism

import { isGraphIsomorphic, findAllIsomorphisms } from "@graphty/algorithms";

// Check if two graphs are isomorphic
const result = isGraphIsomorphic(graph1, graph2, {
    nodeMatch: (node1: NodeId, node2: NodeId, g1: Graph, g2: Graph) => boolean,
    edgeMatch: (edge1: [NodeId, NodeId], edge2: [NodeId, NodeId], g1: Graph, g2: Graph) => boolean,
    findAllMappings: boolean, // Find all possible isomorphisms
});
// Returns: IsomorphismResult { isIsomorphic: boolean, mapping?: Map<NodeId, NodeId> }

// Find all isomorphism mappings
const mappings = findAllIsomorphisms(graph1, graph2, options);
// Returns: Array<Map<NodeId, NodeId>>

Link Prediction Algorithms

Common Neighbors

import { commonNeighborsScore, commonNeighborsPrediction, commonNeighborsForPairs } from "@graphty/algorithms";

// Score for a specific pair
const score = commonNeighborsScore(graph, node1, node2);
// Returns: number

// Predict links for all non-connected pairs
const predictions = commonNeighborsPrediction(graph, {
    directed: boolean, // Consider direction
    includeExisting: boolean, // Include existing edges
    topK: number, // Return only top K predictions
});
// Returns: LinkPredictionScore[]

// Score multiple specific pairs
const scores = commonNeighborsForPairs(graph, pairs, options);
// Returns: LinkPredictionScore[]

// Evaluate prediction performance
const evaluation = evaluateCommonNeighbors(graph, testEdges);
// Returns: { precision, recall, f1Score }

// Get top candidates for a node
const candidates = getTopCandidatesForNode(graph, nodeId, { topK: number });
// Returns: LinkPredictionScore[]

Adamic-Adar Index

import { adamicAdarScore, adamicAdarPrediction, adamicAdarForPairs } from "@graphty/algorithms";

// Adamic-Adar score for a pair (weighted by neighbor degrees)
const score = adamicAdarScore(graph, node1, node2);
// Returns: number

// Predict links using Adamic-Adar
const predictions = adamicAdarPrediction(graph, {
    directed: boolean,
    includeExisting: boolean,
    topK: number,
});
// Returns: LinkPredictionScore[]

// Score multiple pairs
const scores = adamicAdarForPairs(graph, pairs, options);
// Returns: LinkPredictionScore[]

// Compare Adamic-Adar with Common Neighbors
const comparison = compareAdamicAdarWithCommonNeighbors(graph, pairs);
// Returns: Array<{ source, target, adamicAdar, commonNeighbors }>

// Evaluate prediction performance
const evaluation = evaluateAdamicAdar(graph, testEdges);
// Returns: { precision, recall, f1Score }

// Get top candidates for a node
const candidates = getTopAdamicAdarCandidatesForNode(graph, nodeId, {
    topK: number,
});
// Returns: LinkPredictionScore[]

Research Algorithms (2023-2025)

Cutting-edge graph algorithms based on recent research.

SynC - Synergistic Deep Graph Clustering

import { syncClustering } from "@graphty/algorithms";

// Deep learning based clustering
const result = syncClustering(graph, {
    k: number, // Number of clusters
    maxIterations: number, // Default: 100
    learningRate: number, // Default: 0.01
    hiddenDim: number, // Default: 64
    randomSeed: number,
});
// Returns: SynCResult {
//   communities: NodeId[][],
//   clusterAssignments: Map<NodeId, number>,
//   embeddings: Map<NodeId, number[]>,
//   iterations: number,
//   converged: boolean
// }

TeraHAC - Scalable Hierarchical Agglomerative Clustering

import { teraHAC } from "@graphty/algorithms";

// Scalable hierarchical clustering
const result = teraHAC(graph, {
    linkage: "single" | "complete" | "average", // Default: 'average'
    k: number, // Target number of clusters
    threshold: number, // Distance threshold for merging
    sampleSize: number, // Default: 1000
    randomSeed: number,
});
// Returns: TeraHACResult {
//   root: TeraHACClusterNode,
//   dendrogram: TeraHACClusterNode[],
//   clusters: NodeId[][],
//   mergeDistances: number[]
// }

GRSBM - Greedy Recursive Spectral Bisection with Modularity

import { grsbm } from "@graphty/algorithms";

// Explainable community detection
const result = grsbm(graph, {
    minClusterSize: number, // Default: 5
    maxDepth: number, // Default: 10
    modularityThreshold: number, // Default: 0.1
    explainClusters: boolean, // Default: true
});
// Returns: GRSBMResult {
//   clusters: GRSBMCluster[],   // Each cluster has id, nodes, modularity, explanation
//   hierarchy: Map<number, number[]>,
//   totalModularity: number
// }

Algorithm Categories Summary

Available Algorithms by Category:

• Traversal: BFS, DFS, Topological Sort, Cycle Detection, Bipartite Check
• Shortest Path: Dijkstra, Bellman-Ford, Floyd-Warshall, A*
• Centrality: Degree, Betweenness, Closeness, PageRank, Eigenvector, Katz, HITS
• Components: Connected, Strongly Connected, Weakly Connected, Condensation Graph
• Community Detection: Louvain, Leiden, Label Propagation, Girvan-Newman
• Clustering: Hierarchical, K-Core, Spectral, Markov (MCL)
• Minimum Spanning Tree: Kruskal, Prim
• Network Flow: Ford-Fulkerson, Edmonds-Karp, Min-Cut (Stoer-Wagner, Karger)
• Matching: Bipartite Matching, Graph Isomorphism
• Link Prediction: Common Neighbors, Adamic-Adar
• Research Algorithms: SynC, TeraHAC, GRSBM

Interactive Examples

Storybook (Recommended)

Explore algorithms with interactive Storybook demos: View Storybook →

Storybook provides:

• Animated visualizations showing how each algorithm works step-by-step
• Interactive controls to modify parameters and graph types
• Deterministic output with seeded randomness for reproducibility
• Visual testing with Chromatic for regression detection

Legacy HTML Examples

Try out all algorithms with interactive visualizations: Live Demo →

The library includes comprehensive examples demonstrating each algorithm. You can:

• Browse Interactive HTML Examples - Visual demonstrations with step-by-step execution
• View Performance Benchmarks - Comparative analysis of algorithm performance
• Explore Code Examples - Implementation examples for each algorithm

Basic Algorithms

• BFS Traversal - Breadth-first search and shortest paths
• DFS Traversal - Depth-first search and applications
• Dijkstra's Algorithm - Weighted shortest paths
• Bellman-Ford - Shortest paths with negative weights
• Floyd-Warshall - All pairs shortest paths

Centrality Measures

• Degree Centrality - Node importance by connections
• Betweenness Centrality - Bridge nodes
• Closeness Centrality - Central nodes
• PageRank - Node ranking algorithm
• Eigenvector Centrality - Influence from important nodes
• Katz Centrality - Weighted path counting
• HITS Algorithm - Hub and authority scores

Graph Structure

• Connected Components - Find graph components
• Kruskal's MST - Minimum spanning tree
• Prim's MST - Alternative MST algorithm

Community Detection

• Louvain Method - Modularity-based communities
• Leiden Algorithm - Improved Louvain
• Label Propagation - Fast community detection
• Girvan-Newman - Hierarchical communities

Clustering

• Hierarchical Clustering - Graph clustering
• K-Core Decomposition - Core analysis
• Spectral Clustering - Eigenvalue-based clustering
• MCL Clustering - Markov clustering

Matching

• Bipartite Matching - Job assignment, dating apps
• Graph Isomorphism - Structural equivalence

Link Prediction

• Common Neighbors - Friend suggestions
• Adamic-Adar - Weighted predictions

Advanced Algorithms

• A* Pathfinding - Heuristic pathfinding
• Flow Algorithms - Maximum flow and applications
• Ford-Fulkerson Flow - Maximum flow implementation
• Minimum Cut - Graph partitioning

Research Algorithms

• SynC Clustering - Deep learning based clustering
• TeraHAC - Scalable hierarchical clustering
• GRSBM - Explainable community detection

Advanced Usage Examples

Working with Weighted Graphs

const graph = new Graph();

// Add weighted edges
graph.addEdge("A", "B", 5);
graph.addEdge("B", "C", 3);
graph.addEdge("A", "C", 10);

// Find shortest path considering weights
const result = dijkstra(graph, "A");
const pathToC = dijkstraPath(graph, "A", "C");
console.log(pathToC); // { path: ['A', 'B', 'C'], distance: 8 }

Directed Graphs

const directedGraph = new Graph({ directed: true });

directedGraph.addEdge("A", "B");
directedGraph.addEdge("B", "C");
directedGraph.addEdge("C", "A");

// Check for cycles
console.log(hasCycleDFS(directedGraph)); // true

// Find strongly connected components
const sccs = stronglyConnectedComponents(directedGraph);
console.log(sccs.components); // [['A', 'B', 'C']]

Network Analysis

// Identify important nodes
const graph = createSocialNetwork(); // Your graph

// Find influencers (high PageRank)
const influencers = topPageRankNodes(graph, 10);

// Find bridges (high betweenness)
const bridgers = Array.from(betweennessCentrality(graph).entries())
    .sort((a, b) => b[1] - a[1])
    .slice(0, 10);

// Find communities (connected components)
const communities = connectedComponents(graph);
console.log(`Found ${communities.components.length} communities`);

Custom Edge Properties

const graph = new Graph();

// Add edges with custom data
graph.addEdge("A", "B", 1, {
    type: "road",
    distance: 100,
    traffic: "heavy",
});

// Use custom weight in algorithms
const result = dijkstra(graph, "A", {
    weightKey: "distance", // Use 'distance' property as weight
});

Graph Visualization Preparation

// Prepare data for visualization
const graph = loadGraph();

// Calculate layout metrics
const centralities = degreeCentrality(graph, { normalized: true });
const ranks = pageRank(graph);

// Export for visualization
const nodes = Array.from(graph.nodes()).map((node) => ({
    id: node.id,
    data: node.data,
    size: centralities.get(node.id) || 0,
    importance: ranks.get(node.id) || 0,
}));

const edges = Array.from(graph.edges()).map((edge) => ({
    source: edge.source,
    target: edge.target,
    weight: edge.weight || 1,
    data: edge.data,
}));

Type Definitions

Core Types

type NodeId = string | number;

interface Node {
    id: NodeId;
    data?: Record<string, unknown>;
}

interface Edge {
    source: NodeId;
    target: NodeId;
    weight?: number;
    id?: string;
    data?: Record<string, unknown>;
}

Algorithm Result Types

interface TraversalResult {
    visited: Set<NodeId>;
    order: NodeId[];
    tree?: Map<NodeId, NodeId | null>;
}

interface ShortestPathResult {
    distance: number;
    path: NodeId[];
    predecessor: Map<NodeId, NodeId | null>;
}

interface BellmanFordResult {
    distances: Map<NodeId, number>;
    previous: Map<NodeId, NodeId | null>;
    hasNegativeCycle: boolean;
    negativeCycleNodes?: NodeId[];
}

type CentralityResult = Record<string, number>;

interface PageRankResult {
    ranks: Record<string, number>;
    iterations: number;
    converged: boolean;
}

interface CommunityResult {
    communities: Map<NodeId, number>;
    modularity: number;
}

interface ComponentResult {
    components: NodeId[][];
    componentMap: Map<NodeId, number>;
}

interface HITSResult {
    hubs: CentralityResult;
    authorities: CentralityResult;
}

interface SpectralClusteringResult {
    communities: NodeId[][];
    clusterAssignments: Map<NodeId, number>;
}

interface MCLResult {
    communities: NodeId[][];
    attractors: Set<NodeId>;
    iterations: number;
    converged: boolean;
}

interface BipartiteMatchingResult {
    matching: Map<NodeId, NodeId>;
    size: number;
}

interface LinkPredictionScore {
    source: NodeId;
    target: NodeId;
    score: number;
}

interface HierarchicalClusteringResult<T> {
    root: ClusterNode<T>;
    dendrogram: ClusterNode<T>[];
    clusters: Map<number, Set<T>[]>;
}

interface KCoreResult<T> {
    cores: Map<number, Set<T>>;
    coreness: Map<T, number>;
    maxCore: number;
}

interface IsomorphismResult {
    isIsomorphic: boolean;
    mapping?: Map<NodeId, NodeId>;
}

interface SynCResult {
    communities: NodeId[][];
    clusterAssignments: Map<NodeId, number>;
    embeddings: Map<NodeId, number[]>;
    iterations: number;
    converged: boolean;
}

interface TeraHACResult {
    root: TeraHACClusterNode;
    dendrogram: TeraHACClusterNode[];
    clusters: NodeId[][];
    mergeDistances: number[];
}

interface GRSBMResult {
    clusters: GRSBMCluster[];
    hierarchy: Map<number, number[]>;
    totalModularity: number;
}

Performance Considerations

• Graph Representation: Uses adjacency lists for O(1) neighbor access
• Algorithm Complexity:
  • BFS/DFS: O(V + E)
  • Dijkstra: O((V + E) log V) with binary heap
  • Bellman-Ford: O(VE)
  • Floyd-Warshall: O(V³)
  • PageRank: O(k(V + E)) where k is iterations
  • Connected Components: O(V + E)
  • Kruskal's MST: O(E log E)
  • Prim's MST: O((V + E) log V)
  • A*: O((V + E) log V) - depends on heuristic quality
  • Ford-Fulkerson: O(E * f) where f is max flow
  • Edmonds-Karp: O(VE²)
  • Louvain/Leiden: O(n log n) average case
  • Hierarchical Clustering: O(n² log n)
  • SynC: O(kni) where k is clusters, n is nodes, i is iterations
  • TeraHAC: O(n log n) with sampling
  • GRSBM: O(m log n) where m is edges
• Memory Usage: O(V + E) for graph storage
• Browser Optimization: Algorithms use iterative approaches where possible to avoid stack overflow
• Performance Benchmarks: View detailed performance comparisons at https://graphty.app/algorithms/benchmarks/

Development

Prerequisites

• Node.js 18+
• npm 9+

Setup

# Clone the repository
git clone https://github.com/graphty-org/algorithms.git
cd algorithms

# Install dependencies
npm install

# Set up git hooks
npm run prepare

Scripts

# Development
npm run dev          # Watch mode compilation
npm run build        # Build the library
npm run typecheck    # Type checking

# Testing
npm run test         # Run tests in watch mode
npm run test:run     # Run tests once
npm run test:coverage # Generate coverage report
npm run test:browser # Run browser tests

# Code Quality
npm run lint         # Run ESLint
npm run lint:fix     # Fix ESLint issues
npm run lint:pkg     # Check for unused dependencies

# Benchmarking
npm run benchmark    # Run full benchmark suite
npm run benchmark:quick # Run quick benchmark
npm run benchmark:report # Generate performance report

# HTML Examples & Documentation
npm run examples:html # Run interactive HTML examples locally
npm run build:gh-pages # Build for GitHub Pages deployment
npm run examples:run # Run all code examples

# Git
npm run commit       # Conventional commit helper

Development Server

The project includes interactive HTML examples demonstrating each algorithm. To run them locally:

1. Copy the environment configuration:

   cp .env.example .env

2. Configure the server (optional): Edit .env to set your preferred host and port:

   # Server host (defaults to true for network exposure)
   HOST=localhost       # For local-only access
   # HOST=0.0.0.0       # For network access
   # HOST=my.server.com # Custom domain
   
   # Server port (defaults to 9000)
   PORT=9000           # Must be between 9000-9099

3. Start the development server:

   npm run examples:html

4. Open your browser to http://localhost:9000 (or your configured host/port)

The HTML examples provide:

• Interactive visualizations for each algorithm
• Step-by-step execution with play/pause controls
• Multiple graph types for testing
• Real-time parameter adjustment
• Educational information about complexity and use cases
• Mobile debugging console (Eruda) for testing on mobile devices

Project Structure

src/
├── core/              # Core graph data structures
├── algorithms/        # Algorithm implementations
│   ├── traversal/     # BFS, DFS
│   ├── shortest-path/ # Dijkstra, Bellman-Ford
│   ├── centrality/    # Degree, Betweenness, PageRank
│   └── components/    # Connected components
├── data-structures/   # Supporting data structures
├── types/            # TypeScript type definitions
└── utils/            # Utility functions

examples/
├── html/             # Interactive HTML examples
│   ├── shared/       # Shared utilities and styles
│   └── algorithms/   # Algorithm-specific examples

test/
├── unit/             # Unit tests
├── browser/          # Browser-specific tests
└── helpers/          # Test utilities

Contributing

We welcome contributions! Please see our Contributing Guide for details.

Commit Convention

This project uses Conventional Commits:

feat(scope): add new algorithm
fix(scope): resolve edge case in traversal
docs(scope): update API documentation
test(scope): add coverage for centrality measures

License

MIT © Adam Powers

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