@thi.ng/adjacency/README.md

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

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# ![@thi.ng/adjacency](https://raw.githubusercontent.com/thi-ng/umbrella/develop/assets/banners/thing-adjacency.svg?74dfa3d1)

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> [!NOTE]
> This is one of 210 standalone projects, maintained as part
> of the [@thi.ng/umbrella](https://github.com/thi-ng/umbrella/) monorepo
> and anti-framework.
>
> 🚀 Please help me to work full-time on these projects by [sponsoring me on
> GitHub](https://github.com/sponsors/postspectacular). Thank you! ❤️

- [About](#about)
  - [Graph implementations](#graph-implementations)
  - [Traversals](#traversals)
- [Status](#status)
- [Related packages](#related-packages)
- [Installation](#installation)
- [Dependencies](#dependencies)
- [Usage examples](#usage-examples)
- [API](#api)
  - [Basic usage](#basic-usage)
- [Authors](#authors)
- [License](#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](https://thi.ng/disjoint-set)

### Graph implementations

The following types all implement the [`IGraph`
interface](https://docs.thi.ng/umbrella/adjacency/interfaces/IGraph.html) and
support both directed & undirected graphs:

- [AdjacencyBitMatrix (bit matrix based)](https://docs.thi.ng/umbrella/adjacency/classes/AdjacencyBitMatrix.html)
- [AdjacencyMatrix (sparse matrix based)](https://docs.thi.ng/umbrella/adjacency/classes/AdjacencyMatrix.html)
- [AdjacencyList](https://docs.thi.ng/umbrella/adjacency/classes/AdjacencyList.html)

### Traversals

- [Breadth-First Search](https://docs.thi.ng/umbrella/adjacency/functions/bfs.html)
- [Depth-First Search](https://docs.thi.ng/umbrella/adjacency/functions/dfs.html)
- [Floyd-Warshall (global shortest paths search)](https://docs.thi.ng/umbrella/adjacency/functions/floydWarshall.html)
- [Minimum Spanning Tree](https://docs.thi.ng/umbrella/adjacency/functions/mst.html)

## Status

**STABLE** - used in production

[Search or submit any issues for this package](https://github.com/thi-ng/umbrella/issues?q=%5Badjacency%5D+in%3Atitle)

## Related packages

- [@thi.ng/dgraph](https://github.com/thi-ng/umbrella/tree/develop/packages/dgraph) - Type-agnostic directed acyclic graph (DAG) & graph operations

## Installation

```bash
yarn add @thi.ng/adjacency
```

ESM import:

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

Browser ESM import:

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

[JSDelivr documentation](https://www.jsdelivr.com/)

For Node.js REPL:

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

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

## Dependencies

- [@thi.ng/api](https://github.com/thi-ng/umbrella/tree/develop/packages/api)
- [@thi.ng/arrays](https://github.com/thi-ng/umbrella/tree/develop/packages/arrays)
- [@thi.ng/bitfield](https://github.com/thi-ng/umbrella/tree/develop/packages/bitfield)
- [@thi.ng/dcons](https://github.com/thi-ng/umbrella/tree/develop/packages/dcons)
- [@thi.ng/disjoint-set](https://github.com/thi-ng/umbrella/tree/develop/packages/disjoint-set)
- [@thi.ng/errors](https://github.com/thi-ng/umbrella/tree/develop/packages/errors)
- [@thi.ng/sparse](https://github.com/thi-ng/umbrella/tree/develop/packages/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](https://github.com/thi-ng/umbrella/tree/develop/examples)
directory is using this package:

| Screenshot                                                                                                              | Description                                                                      | Live demo                                              | Source                                                                              |
|:------------------------------------------------------------------------------------------------------------------------|:---------------------------------------------------------------------------------|:-------------------------------------------------------|:------------------------------------------------------------------------------------|
| <img src="https://raw.githubusercontent.com/thi-ng/umbrella/develop/assets/examples/geom-voronoi-mst.jpg" width="240"/> | Poisson-disk shape-aware sampling, Voronoi & Minimum Spanning Tree visualization | [Demo](https://demo.thi.ng/umbrella/geom-voronoi-mst/) | [Source](https://github.com/thi-ng/umbrella/tree/develop/examples/geom-voronoi-mst) |

## API

[Generated API docs](https://docs.thi.ng/umbrella/adjacency/)

TODO

### Basic usage

```ts tangle:export/readme.ts
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:

![example graph](https://raw.githubusercontent.com/thi-ng/umbrella/develop/assets/adjacency/readme.png)

## Authors

- [Karsten Schmidt](https://thi.ng) (Main author)
- [Igor Loskutov](https://github.com/Firfi)

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

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

## License

&copy; 2018 - 2025 Karsten Schmidt // Apache License 2.0