Ruby Graph Library (RGL)

RGL is a framework for graph data structures and algorithms.

The design of the library is much influenced by the Boost Graph Library (BGL) which is written in C++ heavily using its template mechanism. Refer to for further links and documentation on graph data structures and algorithms and the design rationales of BGL.

A comprehensive summary of graph terminology can be found in the the graph section of the Dictionary of Algorithms and Data Structures at

Design principles

This document concentrates on the special issues of the implementation in Ruby. The main design goals directly taken from the BGL design are:

  • An interface for how the structure of a graph can be accessed using a generic interface that hides the details of the graph data structure implementation. This interface is defined by the module Graph, which should be included in concrete classes.
  • A standardized generic interface for traversing graphs (RGL::GraphIterator)

RGL provides some general purpose graph classes that conform to this interface, but they are not meant to be the only graph classes. As in BGL I believe that the main contribution of the RGL is the formulation of this interface.

The BGL graph interface and graph components are generic in the sense of the C++ Standard Template Library (STL). In Ruby other techniques are available to express the generic character of the algorithms and data structures mainly using mixins and iterators. The BGL documentation mentions three means to achieve genericity:

  • Algorithm/Data-Structure Interoperability
  • Extension through Function Objects and Visitors
  • Element Type Parameterization
  • Vertex and Edge Property Multi-Parameterization

The first is easily achieved in RGL using mixins, which of course is not as efficient than C++ templates (but much more readable :-). The second one is even more easily implemented using standard iterators with blocks or using the Stream module. The third one is no issue since Ruby is dynamically typed: Each object can be a graph vertex. There is no need for a vertex (or even edge type). In the current version of RGL properties of vertices are simply attached using hashes. At first there seems to be not much need for the graph property machinery.


The first version of RGL only contains a core set of algorithm patterns:

The algorithm patterns by themselves do not compute any meaningful quantities over graphs, they are merely building blocks for constructing graph algorithms. The graph algorithms in RGL currently include:

  • Topological Sort (RGL::TopsortIterator)
  • Connected Components (RGL::Graph#each_connected_component)
  • Strongly Connected Components (RGL::Graph#strongly_connected_components)
  • Transitive Closure (RGL::Graph#transitive_closure)

Data Structures

RGL currently provides two graph classes that implement a generalized adjacency list and an edge list adaptor.

The AdjacencyGraph class is the general purpose *swiss army knife* of graph classes. It is highly parameterized so that it can be optimized for different situations: the graph is directed or undirected, allow or disallow parallel edges, efficient access to just the out-edges, fast vertex insertion and removal at the cost of extra space overhead, etc.

Differences to BGL

The concepts of IncidenceGraph, AdjacencyGraph and VertexListGraph (see are here bundled in the base graph module. Most methods of IncidenceGraph should be standard in the base module Graph. The complexity guarantees can not necessarily provided. See


RGL is depended on the stream library which can also be downloaded from If you use gem to install RGL the stream library will be installed as a prerequisite.

GEM Installation

Download the GEM file and install it with ..

  % gem install rgl-VERSION.gem

or directly with

  % gem install rgl

Use the correct version number for VERSION (e.g. 0.2.x). You may need root privileges to install.

Running tests

RGL comes with a Rakefile which automatically runs the tests. Goto the installation directory and start rake:

 % gem env
 Rubygems Environment:
  - VERSION: 0.9.0 (0.9.0)
  - INSTALLATION DIRECTORY: /usr/lib/ruby/gems/1.8
     - /usr/lib/ruby/gems/1.8

 % cd /usr/lib/ruby/gems/1.8/gems/rgl-0.3.0/
 % rake
 (in /usr/lib/ruby/gems/1.8/gems/rgl-0.3.0)
 /usr/bin/ruby1.8 -Ilib:tests "/usr/lib/ruby/gems/1.8/gems/rake-0.7.3/lib/rake/rake_test_loader.rb" "tests/TestTransitiveClosure.rb" "tests/TestComponents.rb" "tests/TestCycles.rb" "tests/TestDirectedGraph.rb" "tests/TestEdge.rb" "tests/TestGraph.rb" "tests/TestGraphXML.rb" "tests/TestImplicit.rb" "tests/TestUnDirectedGraph.rb" "tests/TestTraversal.rb" "tests/TestDot.rb" "tests/TestRdot.rb"
 Loaded suite /usr/lib/ruby/gems/1.8/gems/rake-0.7.3/lib/rake/rake_test_loader
 Finished in 0.750958 seconds.

 86 tests, 625 assertions, 0 failures, 0 errors

Code coverage

Running rcov on the test suite generates this result.

Normal Installation

You have to install stream library before. You can than install RGL with the following command:

  % ruby install.rb

from its distribution directory. To uninstall it use

  % ruby install.rb -u

Example irb session with RGL

  irb> require 'rgl/adjacency'
  irb> dg=RGL::DirectedAdjacencyGraph[1,2 ,2,3 ,2,4, 4,5, 6,4, 1,6]
  # Use DOT to visualize this graph:
  irb> require 'rgl/dot'
  irb> dg.write_to_graphic_file('jpg')

The result:

  irb> dg.directed?
  irb> dg.vertices
  [5, 6, 1, 2, 3, 4]
  irb> dg.has_vertex? 4

Every object could be a vertex (there is no class Vertex), even the class object Object:

  irb> dg.has_vertex? Object
  irb> dg.edges.sort.to_s
  irb> dg.to_undirected.edges.sort.to_s

Add inverse edge (4-2) to directed graph:

  irb> dg.add_edge 4,2

(4-2) == (2-4) in the undirected graph:

  irb> dg.to_undirected.edges.sort.to_s

(4-2) != (2-4) in directed graphs:

  irb> dg.edges.sort.to_s
  irb> dg.remove_edge 4,2

Topological sort is realized with as iterator:

  require 'rgl/topsort'
  irb> dg.topsort_iterator.to_a
  [1, 2, 3, 6, 4, 5]

A more elaborated example showing implicit graphs:

  def module_graph { |g|
          g.vertex_iterator { |b|
                ObjectSpace.each_object(Module, &b)
          g.adjacent_iterator { |x, b|
                x.ancestors.each { |y|
         unless x == y || y == Kernel || y == Object
          g.directed = true

This function creates a directed graph, with vertices being all loaded modules:

  g = module_graph

We only want to see the ancestors of RGL::AdjacencyGraph:

  tree = bfs_search_tree_from(g,RGL::AdjacencyGraph)

Now we want to visualize this component of g with DOT. We therefore create a subgraph of the original graph, using a filtered graph:

  g = g.vertices_filtered_by {|v| tree.has_vertex? v}

Create the graphics with DOT:


produces module_graph.jpg:

Look for more in the examples directory (i.e. examples.rb).

My links concerning RGL

I collect some links to stuff around RGL at I registered RGL at SWiK.


Many thanks to Robert Feldt which also worked on a graph library ( who pointed me to BGL and many other graph resources.

Robert kindly allowed to integrate his work on graphr, which I did not yet succeed. Especially his work to output graphs for GraphViz is much more elaborated than the minimal support in dot.rb.

Jeremy Siek one of the authors of the nice book "The Boost Graph Library (BGL)" ( kindly allowed to use the BGL documentation as a cheap reference for RGL. He and Robert also gave feedback and many ideas for RGL.

Dave Thomas for RDoc which generated what you read and matz for Ruby. Dave included in the latest version of RDoc (alpha9) the module dot/dot.rb which I use instead of Roberts module to visualize graphs (see rgl/dot.rb).

Jeremy Bopp, John Carter, Sascha Doerdelmann and Shawn Garbett for contributing additions, test cases and bugfixes.


RGL is Copyright (c) 2002,2004,2005,2008 by Horst Duchene. It is free software, and may be redistributed under the terms specified in the README file of the Ruby distribution.


Please contact me at with bug reports suggestions, and other comments. If you send patches, it would help if they were in-line (not attachments) and generated using "diff -u".