A mathematical graph/network library written in PHP

v0.9.0 2015-03-07 18:11 UTC


A mathematical graph/network library written in PHP

Quickstart examples

Once installed, let's initialize a sample graph:

require_once 'vendor/autoload.php';

use \Fhaculty\Graph\Graph as Graph;

$graph = new Graph();

// create some cities
$rome = $graph->createVertex('Rome');
$madrid = $graph->createVertex('Madrid');
$cologne = $graph->createVertex('Cologne');

// build some roads
// create loop

Let's see which city (Vertex) has road (i.e. an edge pointing) to Rome

foreach ($rome->getVerticesEdgeFrom() as $vertex) {
    echo $vertex->getId().' leads to rome'.PHP_EOL;
    // result: Madrid and Rome itself


This library is built around the concept of mathematical graph theory (i.e. it is not a charting library for drawing a graph of a function). In essence, a graph is a set of nodes with any number of connections in between. In graph theory, vertices (plural of vertex) are an abstract representation of these nodes, while connections are represented as edges. Edges may be either undirected ("two-way") or directed ("one-way", aka di-edges, arcs).

Depending on how the edges are constructed, the whole graph can either be undirected, can be a directed graph (aka digraph) or be a mixed graph. Edges are also allowed to form loops (i.e. an edge from vertex A pointing to vertex A again). Also, multiple edges from vertex A to vertex B are supported as well (aka parallel edges), effectively forming a multigraph (aka pseudograph). And of course, any combination thereof is supported as well. While many authors try to differentiate between these core concepts, this library tries hard to not impose any artificial limitations or assumptions on your graphs.


This library provides the core data structures for working with graphs, its vertices, edges and attributes.

There are several official components built on top of these structures to provide commonly needed functionality. This architecture allows these components to be used independently and on demand only.

Following is a list of some highlighted components. A list of all official components can be found in the graphp project.

Graph drawing

This library is built to support visualizing graph images, including them into webpages, opening up images from within CLI applications and exporting them as PNG, JPEG or SVG file formats (among many others). Because graph drawing is a complex area on its own, the actual layouting of the graph is left up to the excellent GraphViz "Graph Visualization Software" and we merely provide some convenient APIs to interface with GraphViz.

See graphp/graphviz for more details.

Common algorithms

Besides graph drawing, one of the most common things to do with graphs is running algorithms to solve common graph problems. Therefore this library is being used as the basis for implementations for a number of commonly used graph algorithms:

  • Search
    • Deep first (DFS)
    • Breadth first search (BFS)
  • Shortest path
    • Dijkstra
    • Moore-Bellman-Ford (MBF)
    • Counting number of hops (simple BFS)
  • Minimum spanning tree (MST)
    • Kruskal
    • Prim
  • Traveling salesman problem (TSP)
    • Bruteforce algorithm
    • Minimum spanning tree heuristic (TSP MST heuristic)
    • Nearest neighbor heuristic (NN heuristic)
  • Maximum flow
  • Minimum cost flow (MCF)
    • Cycle canceling
    • Successive shortest path
  • Maximum matching
    • Flow algorithm

See graphp/algorithms for more details.


The recommended way to install this library is through composer. New to composer?

    "require": {
        "clue/graph": "~0.9.0"

You may also want to install some of the additional components. A list of all official components can be found in the graphp project.


This library uses PHPUnit for its extensive test suite. You can either use a global installation or rely on the one composer installs when you first run $ composer install. This sets up the developer environment, so that you can now run it from the project root directory:

$ php vendor/bin/phpunit


This library comes with an extensive test suite and is regularly tested and used in the real world. Despite this, this library is still considered beta software and its API is subject to change. The changelog lists all relevant information for updates between releases.

If you encounter any issues, please don't hesitate to drop us a line, file a bug report or even best provide us with a patch / pull request and/or unit test to reproduce your problem.

Besides directly working with the code, any additional documentation, additions to our readme or even fixing simple typos are appreciated just as well.

Any feedback and/or contribution is welcome!

Check out #graphp on


Released under the terms of the permissive MIT license.