Yograph 🌳

যোগ • (jōg) noun

connection, link, union

addition, sum

Yograph is a pure Dart graph algorithms and data structures library. It supports directed and undirected graphs, weighted graphs, traversal, shortest paths, minimum spanning trees, network flow, centrality, community detection, DAG algorithms, graph generators, I/O, and rendering.

Algorithms operate on capability-based interfaces, so custom graph representations can plug into the same APIs.

YogEx — Elixir implementation.
Yog — Gleam implementation.

Features

Yograph includes algorithms for the following areas:

Pathfinding & Shortest Paths

Dijkstra — Dijkstra.shortestPath(), Dijkstra.singleSourceDistances()
A* — AStar.aStar(), AStar.implicitAStar(), AStar.implicitAStarBy()
Bellman-Ford — BellmanFord.shortestPath(), negative cycle detection
Floyd-Warshall — FloydWarshall.allPairs(), all-pairs shortest paths
Johnson — Johnson.allPairs(), all-pairs shortest paths with negative weights (no negative cycles)
Bidirectional Dijkstra — BidirectionalDijkstra.shortestPath(), single-pair shortest path search Bidirectional BFS — BidirectionalBfs.shortestPath(), fewest-edge single-pair search
Yen's K-Shortest — Yen.kShortestPaths(), up to k shortest loopless paths
Widest Path — Dijkstra.widestPath(), maximum bottleneck routing

Weighted algorithms support custom edge-weight semantics through WeightAlgebra<E>. Built-in algebras cover common numeric weights (double and int), while custom algebras let algorithms work with domain-specific edge data.

Traversal

BFS & DFS — walk(), walkUntil(), foldWalk()
Best-First — bestFirstWalk(), bestFirstFold()
Topological Sort — topologicalSort(), lexicographicalTopologicalSort()
Random Walk — randomWalk() with optional seed

Connectivity & Structure

Connected Components — Components.connectedComponents(), Components.weaklyConnectedComponents()
Strongly Connected Components — SCC.tarjan(), SCC.kosaraju()
Bridge & Articulation Point Detection — Analysis.analyze()
K-Core Decomposition — KCore.detect(), KCore.coreNumbers(), KCore.degeneracy()
Reachability Counts — Reachability.counts() with DAG and SCC condensation implementations Structural Predicates — Structure.isTree(), Structure.isChordal(), Structure.isArborescence(), Structure.isComplete(), Structure.isRegular()

Centrality

Degree — Centrality.degree() with DegreeMode (in / out / total)
Distance-Based — Centrality.closeness(), Centrality.harmonic(), Centrality.betweenness() (Brandes' algorithm)
Spectral / Iterative — Centrality.pageRank(), Centrality.eigenvector(), Centrality.katz(), Centrality.alpha()
Link-Analysis — Centrality.hits() (hub & authority scores)

Health Metrics

Distance Metrics — Health.diameter(), Health.radius(), Health.eccentricity()
Structural — Health.assortativity() (Pearson degree correlation)
Path Metrics — Health.averagePathLength()
Efficiency — Health.globalEfficiency(), Health.localEfficiency(), Health.averageLocalEfficiency()

Minimum Spanning Tree

Kruskal — MST.kruskal(), MST.kruskalMax()
Prim — MST.prim(), MST.primMax()

DAG Algorithms

DAG Detection — DAG.isDag(), DAG.topologicalOrder()
Generations — DAG.topologicalGenerations()
Paths — DAG.longestPath(), DAG.shortestPath(), DAG.pathCount()
Distances — DAG.singleSourceDistances()
Sources & Sinks — DAG.sources(), DAG.sinks()
Ancestry — DAG.ancestors(), DAG.descendants(), DAG.lowestCommonAncestors()

Matching

Bipartite Maximum Matching — Matching.hopcroftKarp()
Bipartite Minimum/Maximum Weight Perfect Matching — Matching.hungarian()
General Maximum Matching — Matching.blossomMaximumMatching() (Edmonds' blossom algorithm)

Community Detection

Louvain — Community.louvain() (modularity optimization, hierarchical variant available)
Leiden — Community.leiden() (Louvain with refinement, hierarchical variant available)
Label Propagation — Community.labelPropagation()
Walktrap — Community.walktrap() (random-walk hierarchical clustering)
Metrics — Community.modularity(), Community.clusteringCoefficient(), Community.averageClusteringCoefficient(), Community.transitivity(), Community.countTriangles()
Utilities — Community.toMap(), Community.sizes(), Community.merge(), Community.nmi()

Graph Transformations

Transitive Closure — Transform.transitiveClosure()
Transitive Reduction — Transform.transitiveReduction()

Design

Capability-Based Interfaces — Traversable, Queryable, Mutable, Reversible combine into roles such as Walkable, WeightedWalkable, and Bidirectional.
Labeled Builder — LabeledBuilder maps string/enum labels to internal int node IDs.
Strategy Pattern — Pathfinding.shortestPath() accepts PointToPointStrategy implementations.
Weight Algebra — WeightAlgebra<E> lets weighted algorithms interpret custom edge data types.
Disjoint Set — DisjointSet with path compression and union by rank.

Installation

Add yograph to your pubspec.yaml:

dependencies:
  yograph: ^0.5.0

Or via command line:

dart pub add yograph

Quick Start

import 'package:yograph/yograph.dart';

void main() {
  // Create a directed graph with String labels on nodes, int weights on edges
  final graph = SimpleGraph<String, int>.directed()
    ..addEdge(0, 1, data: 4)
    ..addEdge(0, 2, data: 2)
    ..addEdge(2, 1, data: 1)
    ..addEdge(1, 3, data: 5)
    ..addEdge(2, 3, data: 8);

  // Find shortest path (default: Dijkstra)
  final path = Pathfinding.shortestPath(graph, 0, 3);
  print(path); // Path(0 -> 2 -> 1 -> 3, weight: 8)

  // Use A* with a heuristic
  final astarPath = Pathfinding.shortestPath(
    graph,
    0,
    3,
    strategy: AStar(heuristic: (node, goal) => (goal - node).abs().toDouble()),
  );
  print(astarPath); // Path(0 -> 2 -> 1 -> 3, weight: 8)

  // Bellman-Ford handles negative weights
  final bfGraph = SimpleGraph<String, int>.directed()
    ..addEdge(0, 1, data: 4)
    ..addEdge(0, 2, data: 3)
    ..addEdge(1, 2, data: -2)
    ..addEdge(2, 3, data: -3);

  final result = BellmanFord.shortestPath(bfGraph, 0, 3);
  if (result.isSuccess) {
    print(result.path); // Path(0 -> 1 -> 2 -> 3, weight: -1)
  } else if (result.hasNegativeCycle) {
    print('Negative cycle detected!');
  }

  // All-pairs shortest paths
  final fw = FloydWarshall.allPairs(graph);
  print(fw.distance(0, 3)); // 8.0

  // Minimum spanning tree (undirected only)
  final undirected = SimpleGraph<String, int>.undirected()
    ..addEdge(0, 1, data: 4)
    ..addEdge(0, 2, data: 1)
    ..addEdge(1, 2, data: 3);

  final mst = MST.kruskal(undirected);
  print(mst.totalWeight); // 4

  // Centrality
  final scores = Centrality.betweenness(undirected);
  print(scores); // {0: 0.0, 1: 0.0, 2: 0.0}

  // Health metrics
  print(Health.diameter(undirected)); // 1.0
  print(Health.assortativity(undirected)); // 0.0 (all same degree)

  // Connectivity
  print(Components.connectedComponents(undirected)); // [[0, 1, 2]]
  print(Structure.isTree(undirected)); // false (has a cycle)
}

Using Labels Instead of Integer IDs

final builder = LabeledBuilder<String, int>.directed()
  ..addEdge('A', 'B', data: 4)
  ..addEdge('A', 'C', data: 2)
  ..addEdge('C', 'B', data: 1);

final graph = builder.toGraph();
final path = Pathfinding.shortestPath(graph, builder.getId('A')!, builder.getId('B')!);
print(path); // Path(0 -> 2 -> 1, weight: 3)

Connectivity & Structure

final graph = SimpleGraph<String, void>.undirected()
  ..addEdge(0, 1)
  ..addEdge(1, 2)
  ..addEdge(2, 0)
  ..addEdge(0, 3);

// Bridges and articulation points
final analysis = Analysis.analyze(graph);
print(analysis.bridges);       // [(0, 3)]
print(analysis.articulationPoints); // {0}

// Strongly connected components (directed)
final directed = SimpleGraph<String, void>.directed()
  ..addEdge(0, 1)
  ..addEdge(1, 2)
  ..addEdge(2, 0)
  ..addEdge(2, 3);

print(SCC.tarjan(directed)); // [[3], [0, 1, 2]]

// K-core decomposition
print(KCore.coreNumbers(graph)); // {0: 2, 1: 2, 2: 2, 3: 1}

// Structural predicates
print(Structure.isChordal(graph)); // true
print(Structure.isComplete(graph)); // false

DAG & Transforms

final dag = SimpleGraph<String, void>.directed()
  ..addEdge(0, 1)
  ..addEdge(0, 2)
  ..addEdge(1, 3)
  ..addEdge(2, 3)
  ..addEdge(0, 3); // shortcut

// Topological generations
print(DAG.topologicalGenerations(dag)); // [[0], [1, 2], [3]]

// Longest path
print(DAG.longestPath(dag)); // [0, 1, 3] or [0, 2, 3]

// Transitive closure
print(Transform.transitiveClosure(dag));
// {0: {0, 1, 2, 3}, 1: {1, 3}, 2: {2, 3}, 3: {3}}

// Transitive reduction removes the redundant shortcut
final reduced = Transform.transitiveReduction(dag)!;
print(reduced.hasEdge(0, 3)); // false

Community Detection

final social = SimpleGraph<String, int>.undirected()
  ..addEdge(0, 1, data: 1)
  ..addEdge(1, 2, data: 1)
  ..addEdge(2, 0, data: 1)
  ..addEdge(3, 4, data: 1)
  ..addEdge(4, 5, data: 1)
  ..addEdge(5, 3, data: 1)
  ..addEdge(2, 3, data: 1); // bridge between two cliques

// Louvain modularity optimization
final communities = Community.louvain(social, seed: 42);
print(communities.numCommunities); // 2
print(Community.modularity(social, communities)); // > 0.3

// Clustering metrics
print(Community.transitivity(social)); // global clustering coefficient
print(Community.averageClusteringCoefficient(social));

// Utilities
print(Community.toMap(communities)); // {0: {0, 1, 2}, 1: {3, 4, 5}}

Matching

// Bipartite maximum cardinality
final bipartite = SimpleGraph<String, void>.undirected()
  ..addEdge(0, 3)
  ..addEdge(0, 4)
  ..addEdge(1, 4)
  ..addEdge(2, 5);

print(Matching.hopcroftKarp(bipartite)); // {0: 3, 1: 4, 2: 5}

// Weighted bipartite matching (Hungarian / Kuhn-Munkres)
final weighted = SimpleGraph<String, int>.undirected()
  ..addEdge(0, 2, data: 1)
  ..addEdge(0, 3, data: 4)
  ..addEdge(1, 2, data: 2)
  ..addEdge(1, 3, data: 3);

final result = Matching.hungarian(weighted, optimization: Optimization.min);
print(result.cost);      // 4.0
print(result.matching);  // {0: 2, 1: 3}

// General graph maximum matching (Edmonds' blossom)
final general = SimpleGraph<String, void>.undirected()
  ..addEdge(0, 1)
  ..addEdge(1, 2)
  ..addEdge(2, 0)
  ..addEdge(2, 3);

print(Matching.blossomMaximumMatching(general)); // {0: 1, 1: 0, 2: 3, 3: 2}

Development

Running Tests

# Full test suite
dart test

# With coverage
dart test --coverage=coverage

# Analyze
dart analyze --fatal-infos

# Format check
dart format --output=none --set-exit-if-changed .

Git Pre-Commit Hook

This repository includes a Git pre-commit hook that formats staged .dart files and runs dart analyze before the commit.

To enable the pre-commit hook in your local clone, run:

git config core.hooksPath .githooks

License

MIT

Yograph 🌳

Features

Pathfinding & Shortest Paths

Traversal

Connectivity & Structure

Centrality

Health Metrics

Minimum Spanning Tree

DAG Algorithms

Matching

Community Detection

Graph Transformations

Design

Installation

Quick Start

Using Labels Instead of Integer IDs

Connectivity & Structure

DAG & Transforms

Community Detection

Matching

Development

Running Tests

Git Pre-Commit Hook

License

Libraries

yograph package