Plexus (was Graphy). A framework for graph theory, graph data structures and associated algorithms.

Graph algorithms currently provided are:

• Topological Sort
• Strongly Connected Components
• Transitive Closure
• Rural Chinese Postman
• Biconnected

These are based on more general algorithm patterns:

• Breadth First Search
• Depth First Search
• A* Search
• Floyd-Warshall
• Best First Search
• Djikstra's Algorithm
• Lexicographic Search

A quick Tour

Arcs

There are two vertices bound classes, Plexus::Arc and Plexus::Edge. The former defines directional edges, the latter undirected edges.

Vertices

Vertices can be any Object.

Graph Types

There are a number of different graph types, each of which provide different features and constraints:

Plexus::Digraph and its alias Plexus::DirectedGraph:

• Single directed edges (arcs) between vertices
• Loops are forbidden

Plexus::DirectedPseudoGraph:

• Multiple directed edges (arcs) between vertices
• Loops are forbidden

Plexus::DirectedMultiGraph:

• Multiple directed edges (arcs) between vertices
• Loops on vertices

Plexus::UndirectedGraph, Plexus::UndirectedPseudoGraph, and Graph::UndirectedMultiGraph are similar but all edges are undirected.

Data Structures

In order to modelize data structures, make use of the Plexus::AdjacencyGraph module which provides a generalized adjacency list and an edge list adaptor.

The Plexus::Digraph class is the general purpose "swiss army knife" of graph classes, most of the other classes are just modifications to this class. It is optimized for efficient access to just the out-edges, fast vertex insertion and removal at the cost of extra space overhead, etc.

Example Usage

Using IRB, first require the library:

require 'rubygems' # only if you are using ruby 1.8.x
require 'plexus'

If you'd like to include all the classes in the current scope (so you don't have to prefix with Plexus::), just:

include Plexus

Let's play with the library a bit in IRB:

>> dg = Digraph[1,2, 2,3, 2,4, 4,5, 6,4, 1,6]
=> Plexus::Digraph[[2, 3], [1, 6], [2, 4], [4, 5], [1, 2], [6, 4]]

A few properties of the graph we just created:

>> dg.directed?
=> true
>> dg.vertex?(4)
=> true
>> dg.edge?(2,4)
=> true
>> dg.edge?(4,2)
=> false
>> dg.vertices
=> [1, 2, 3, 4, 5, 6]

Every object could be a vertex, even the class object Object:

>> dg.vertex?(Object)
=> false

>> UndirectedGraph.new(dg).edges.sort.to_s
=> "[Plexus::Edge[1,2,nil], Plexus::Edge[2,3,nil], Plexus::Edge[2,4,nil],
      Plexus::Edge[4,5,nil], Plexus::Edge[1,6,nil], Plexus::Edge[6,4,nil]]"

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

>> dg.add_edge!(4,2)
=> Plexus::DirectedGraph[Plexus::Arc[1,2,nil], Plexus::Arc[1,6,nil], Plexus::Arc[2,3,nil],
                          Plexus::Arc[2,4,nil], Plexus::Arc[4,5,nil], Plexus::Arc[4,2,nil],
                          Plexus::Arc[6,4,nil]]

(4-2) == (2-4) in the undirected graph (4-2 doesn't show up):

    >> UndirectedGraph.new(dg).edges.sort.to_s
    => "[Plexus::Edge[1,2,nil], Plexus::Edge[2,3,nil], Plexus::Edge[2,4,nil],
         Plexus::Edge[4,5,nil], Plexus::Edge[1,6,nil], Plexus::Edge[6,4,nil]]"

(4-2) != (2-4) in directed graphs (both show up):

>> dg.edges.sort.to_s
=> "[Plexus::Arc[1,2,nil], Plexus::Arc[1,6,nil], Plexus::Arc[2,3,nil],
      Plexus::Arc[2,4,nil], Plexus::Arc[4,2,nil], Plexus::Arc[4,5,nil],
      Plexus::Arc[6,4,nil]]"

>> dg.remove_edge! 4,2
=> Plexus::DirectedGraph[Plexus::Arc[1,2,nil], Plexus::Arc[1,6,nil], Plexus::Arc[2,3,nil],
                          Plexus::Arc[2,4,nil], Plexus::Arc[4,5,nil], Plexus::Arc[6,4,nil]]

Topological sorting is realized with an iterator:

>> dg.topsort
=> [1, 6, 2, 4, 5, 3]
>> y = 0; dg.topsort { |v| y += v }; y
=> 21

You can use DOT to visualize the graph:

>> require 'plexus/dot'
>> dg.write_to_graphic_file('jpg','visualize')

Here's an example showing the module inheritance hierarchy:

>> module_graph = Digraph.new
>> ObjectSpace.each_object(Module) do |m|
>>   m.ancestors.each {|a| module_graph.add_edge!(m,a) if m != a}
>> end
>> gv = module_graph.vertices.select {|v| v.to_s.match(/Plexus/) }
>> module_graph.induced_subgraph(gv).write_to_graphic_file('jpg','module_graph')

Look for more in the examples directory.

History

This library is based on GRATR by Shawn Garbett (itself a fork of Horst Duchene's RGL library) which is heavily influenced by the Boost Graph Library (BGL).

This fork attempts to modernize and extend the API and tests.

References

For more information on Graph Theory, you may want to read:

• the documentation for the Boost Graph Library
• the Dictionary of Algorithms and Data Structures

Credits

See CREDITS.markdown

TODO

See TODO.markdown

CHANGELOG

See CHANGELOG.markdown

License

MIT License. See the LICENSE file.