# 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++. Refer to http://www.boost.org/libs/graph/doc 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 graph section
of the *Dictionary of Algorithms and Data Structures* at
http://www.nist.gov/dads/HTML/graph.html or
Wikipedia.

## Documentation

- RGL's API Reference at http://rubydoc.info

## 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 RGL::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.

### Algorithms

RGL current contains a core set of algorithm patterns:

- Breadth First Search RGL::BFSIterator
- Depth First Search RGL::DFSIterator

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
- Dijkstras Shortest Path Algorithm RGL::DijkstraAlgorithm
- Bellman Ford Algorithm RGL::BellmanFordAlgorithm

### 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 http://www.boost.org/libs/graph/doc/IncidenceGraph.html) 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 http://www.boost.org/libs/graph/doc/graph_concepts.html.

## Installation

```
% gem install rgl
```

or download the latest sources from the git repository http://github.com/monora/rgl.

If you are going to use the drawing functionalities install Graphviz.

## Running tests

Checkout RGL git repository and go to the project directory. First, install RGL dependencies with bundler:

```
% bundle install
```

After that you can run the tests:

```
% rake test
```

## Example irb session with RGL

```
% irb -Ilib
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')
"graph.jpg"
```

The result:

You can control the graph layout by passing layout parameters to `write_to_graphic_file`

. See
`TestDot::test_to_dot_digraph_with_options`

for an example using a feature implemented by Lia
Skalkos (see PR #41).

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

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

```
irb> dg.has_vertex? Object
false
irb> dg.edges.sort.to_s
"(1-2)(1-6)(2-3)(2-4)(4-5)(6-4)"
irb> dg.to_undirected.edges.sort.to_s
"(1=2)(1=6)(2=3)(2=4)(5=4)(6=4)"
```

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
"(1=2)(1=6)(2=3)(2=4)(5=4)(6=4)"
```

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

```
irb> dg.edges.sort.to_s
"(1-2)(1-6)(2-3)(2-4)(4-2)(4-5)(6-4)"
irb> dg.remove_edge 4,2
true
```

Check whether a path exists between vertices 1 and 5

```
irb> require 'rgl/path'
irb> dg.path?(1, 5)
true
```

*Topological sort* is implemented as an iterator:

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

A more elaborated example showing *implicit graphs*:

```
require 'rgl/implicit'
def module_graph
RGL::ImplicitGraph.new { |g|
g.vertex_iterator { |b|
ObjectSpace.each_object(Module, &b)
}
g.adjacent_iterator { |x, b|
x.ancestors.each { |y|
b.call(y) unless x == y || y == Kernel || y == Object
}
}
g.directed = true
}
end
```

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:

```
require 'rgl/traversal'
tree = g.bfs_search_tree_from(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}
g.write_to_graphic_file('jpg')
```

creates the following graph image with DOT:

This graph shows all loaded RGL modules:

Look for more in examples directory.

I collect some links to stuff around RGL at http://del.icio.us/monora/rgl.

## Credits

Many thanks to Robert Feldt which also worked on a graph library (http://rockit.sf.net/subprojects/graphr) 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 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, Shawn Garbett, Andreas SchÃ¶rk and Kirill Lashuk for contributing additions, test cases and bugfixes.

Kirill Lashuk who started to take over further development in November 2012.

See also http://github.com/monora/rgl/contributors.

## Copying

RGL is Copyright (c) 2002,2004,2005,2008,2013,2015,2019,2020 by Horst Duchene. It is free software, and may be redistributed under the Ruby license and terms specified in the LICENSE file.