@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:

``typescript
// 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

$3

| 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._

$3

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

Installation

`bash
npm install @graphty/algorithms
`

Quick Start

`typescript
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

$3

The core data structure for representing graphs.

`typescript
class Graph {
constructor(config?: Partial);
}
`

#### Configuration Options

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

#### Node Operations

`typescript
// Add a node with optional data
graph.addNode(id: NodeId, data?: Record): 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
`

#### Edge Operations

`typescript
// Add an edge with optional weight and data
graph.addEdge(
source: NodeId,
target: NodeId,
weight?: number,
data?: Record
): 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
`

#### Graph Properties

`typescript
// 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

`typescript
// 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

`typescript
// Get neighboring nodes
graph.neighbors(nodeId: NodeId): IterableIterator

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

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

#### Utility Methods

`typescript
// 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
`

$3

#### Breadth-First Search (BFS)

`typescript
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, order: NodeId[], tree?: Map }

// 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 }

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

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

#### Depth-First Search (DFS)

`typescript
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[][]
`

$3

#### Dijkstra's Algorithm

`typescript
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
// ShortestPathResult = { distance: number, path: NodeId[], predecessor: Map }

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

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

// All pairs shortest paths
const allPairs = allPairsShortestPath(graph)
// Returns: Map>
`

#### Bellman-Ford Algorithm

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

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

// 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

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

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

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

// Compute transitive closure
const closure = transitiveClosure(graph);
// Returns: Map>
`

$3

#### Degree Centrality

`typescript
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)

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

#### Betweenness Centrality

`typescript
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)

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

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

#### Closeness Centrality

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

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

// 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)

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

#### PageRank

`typescript
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,
personalization: Record,
});
// Returns: { ranks: Record, iterations: number, converged: boolean }

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

// 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)
`

#### Eigenvector Centrality

`typescript
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)

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

#### Katz Centrality

`typescript
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)

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

#### HITS Algorithm

`typescript
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 }
`

$3

#### Basic Component Operations

`typescript
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
`

#### Strongly Connected Components

`typescript
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 }

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

#### Weakly Connected Components

`typescript
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
`

$3

#### Priority Queue

Min-heap implementation used internally by algorithms.

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

const pq = new PriorityQueue((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.

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

const uf = new UnionFind();

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

$3

#### Kruskal's Algorithm

`typescript
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

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

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

$3

#### Louvain Method

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

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

#### Leiden Algorithm

`typescript
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, modularity: number }
`

#### Label Propagation

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

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

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

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

#### Girvan-Newman Algorithm

`typescript
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[][] }> }
`

$3

#### A\* Algorithm

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

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

$3

#### Maximum Flow

`typescript
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> }

// 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

`typescript
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, sinkPartition: Set }

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

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

$3

#### Hierarchical Clustering

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

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

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

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

#### K-Core Decomposition

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

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

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

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

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

#### Spectral Clustering

`typescript
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 }
`

#### Markov Clustering (MCL)

`typescript
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, iterations: number, converged: boolean }

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

$3

#### Bipartite Matching

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

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

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

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

#### Graph Isomorphism

`typescript
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 }

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

$3

#### Common Neighbors

`typescript
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

`typescript
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[]
`

$3

Cutting-edge graph algorithms based on recent research.

#### SynC - Synergistic Deep Graph Clustering

`typescript
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,
// embeddings: Map,
// iterations: number,
// converged: boolean
// }
`

#### TeraHAC - Scalable Hierarchical Agglomerative Clustering

`typescript
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

`typescript
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,
// totalModularity: number
// }
`

Algorithm Categories Summary

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- 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

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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

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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

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- 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

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- 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

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

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

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

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

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

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

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

Advanced Usage Examples

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`typescript
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 }
`

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`typescript
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']]
`

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`typescript
// 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);
`

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`typescript
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
});
`

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`typescript
// 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

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`typescript
type NodeId = string | number;

interface Node {
id: NodeId;
data?: Record;
}

interface Edge {
source: NodeId;
target: NodeId;
weight?: number;
id?: string;
data?: Record;
}
`

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`typescript
interface TraversalResult {
visited: Set;
order: NodeId[];
tree?: Map;
}

interface ShortestPathResult {
distance: number;
path: NodeId[];
predecessor: Map;
}

interface BellmanFordResult {
distances: Map;
previous: Map;
hasNegativeCycle: boolean;
negativeCycleNodes?: NodeId[];
}

type CentralityResult = Record;

interface PageRankResult {
ranks: Record;
iterations: number;
converged: boolean;
}

interface CommunityResult {
communities: Map;
modularity: number;
}

interface ComponentResult {
components: NodeId[][];
componentMap: Map;
}

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

interface SpectralClusteringResult {
communities: NodeId[][];
clusterAssignments: Map;
}

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

interface BipartiteMatchingResult {
matching: Map;
size: number;
}

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

interface HierarchicalClusteringResult {
root: ClusterNode;
dendrogram: ClusterNode[];
clusters: Map[]>;
}

interface KCoreResult {
cores: Map>;
coreness: Map;
maxCore: number;
}

interface IsomorphismResult {
isIsomorphic: boolean;
mapping?: Map;
}

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

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

interface GRSBMResult {
clusters: GRSBMCluster[];
hierarchy: Map;
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

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- Node.js 18+
- npm 9+

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`bash


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
`

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`bash


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
`

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

1. Copy the environment configuration:

`bash
cp .env.example .env
`

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

`bash
# 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:

`bash
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

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`
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.

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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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