@thi.ng/adjacency

[!NOTE] This is one of 208 standalone projects, maintained as part of the @thi.ng/umbrella monorepo and anti-framework.

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• About
  • Graph implementations
  • Traversals
• Status
• Related packages
• Installation
• Dependencies
• Usage examples
• API
  • Basic usage
• Authors
• License

About

Sparse & bitwise adjacency matrices, lists and selected traversal algorithms for directed & undirected graphs.

[!IMPORTANT] In July 2024 this package was restructured and split-up to extract some features into smaller more focused packages:

• @thi.ng/disjoint-set

Graph implementations

The following types all implement the IGraph interface and support both directed & undirected graphs:

• AdjacencyBitMatrix (bit matrix based)
• AdjacencyMatrix (sparse matrix based)
• AdjacencyList

Traversals

• Breadth-First Search
• Depth-First Search
• Floyd-Warshall (global shortest paths search)
• Minimum Spanning Tree

Status

STABLE - used in production

Search or submit any issues for this package

Related packages

• @thi.ng/dgraph - Type-agnostic directed acyclic graph (DAG) & graph operations

Installation

yarn add @thi.ng/adjacency

ESM import:

import * as adj from "@thi.ng/adjacency";

Browser ESM import:

<script type="module" src="https://esm.run/@thi.ng/adjacency"></script>

JSDelivr documentation

For Node.js REPL:

const adj = await import("@thi.ng/adjacency");

Package sizes (brotli'd, pre-treeshake): ESM: 2.53 KB

Dependencies

• @thi.ng/api
• @thi.ng/arrays
• @thi.ng/bitfield
• @thi.ng/dcons
• @thi.ng/disjoint-set
• @thi.ng/errors
• @thi.ng/sparse

Note: @thi.ng/api is in most cases a type-only import (not used at runtime)

Usage examples

One project in this repo's /examples directory is using this package:

Screenshot	Description	Live demo	Source
	Poisson-disk shape-aware sampling, Voronoi & Minimum Spanning Tree visualization	Demo	Source

API

Generated API docs

TODO

Basic usage

import { defAdjBitMatrix, type Edge } from "@thi.ng/adjacency";

// relationships
const rels = {
    a: ["b", "c"],
    b: ["d"],
    c: ["d", "e"],
    e: ["a", "d", "b"],
};

// form set of unique node IDs
const nodeIDs = [
    ...new Set(Object.entries(rels).flatMap(([id, rels]) => [id, ...rels])),
];

// the current adjacency matrix impls only support numeric node IDs
// therefore, we first map node names to numeric IDs
const index = new Map(nodeIDs.map((id, i) => [id, i]));

// transform relationships into sequence of edges (aka `[from,to]` tuples)
const edges = Object.entries(rels).flatMap(([id, rels]) =>
    rels.map((x) => <Edge>[index.get(id), index.get(x)])
);

// build adjacency matrix, treat as undirected graph
// edges can also be added/removed later
const graph = defAdjBitMatrix(nodeIDs.length, edges, true);

// graph queries
console.log("edges:", graph.numEdges(), "verts:", graph.numVertices());
// edges: 8 verts: 5

// check if vertex/node is present in graph
// (this is implementation specific and for the bitmatrix backed version here
// only true if the vertex has at least 1 edge...)
console.log(graph.hasVertex(index.get("d")!));
// true

// are `a` and `d` connected?
console.log(graph.hasEdge(index.get("a")!, index.get("d")!));
// false

// number of connected nodes for `a`
// (in directed graphs, there's also possibility to distinguish between in/out/inout)
console.log(graph.degree(index.get("a")!));
// 3

// neighbors of `a` (with reverse lookup of node names)
console.log(graph.neighbors(index.get("a")!).map((x) => nodeIDs[x]));
// [ 'b', 'c', 'e' ]

// serialize to GraphViz DOT format (see result visualization below)
console.log(graph.toDot(nodeIDs));
// graph g {
// "d"--"e";
// "c"--"d";
// "c"--"e";
// "b"--"d";
// "b"--"e";
// "a"--"b";
// "a"--"c";
// "a"--"e";
// }

// resize to new capacity & add add/remove vertices/edges
graph.resize(10);

graph.addEdge(4, 5);
graph.removeEdge(0, 1);

GraphViz visualization of the above example graph:

Authors

• Karsten Schmidt (Main author)
• Igor Loskutov

If this project contributes to an academic publication, please cite it as:

@misc{thing-adjacency,
  title = "@thi.ng/adjacency",
  author = "Karsten Schmidt and others",
  note = "https://thi.ng/adjacency",
  year = 2018
}

License

© 2018 - 2025 Karsten Schmidt // Apache License 2.0