Ogr

General graph library for Ruby. Provides sparse(or dense), directed(or undirected) and weighted(or normal) graphs. Graph processing algorithms like BFS, DFS, ShortestPaths, MinimumSpanningTree are also included. This gem depends only on DS Gem which contains other data structures not implemented in Ruby Standard Library.

Installation

  gem install ogr

Usage

  require 'ogr'
  graph = Ogr::Graph.new

To not have to type "Ogr::" before each class:

  include Ogr
  graph = Graph.new

Graph

Creating new Graph is easy.

First define edges(weights are optional):

  edges = []
  edges << Edge.new('Jim','Bob', 12)
  edges << Edge.new('Jim','Tom', 3)
  edges << Edge.new('Bob','Jack', 8)
  edges << Edge.new('Tom','Bob', 5)

or

  edges = [
      ['Jim','Bob', 12],
      ['Jim','Tom', 3],
      ['Bob','Jack', 8],
      ['Tom','Bob', 5]
  ]

Next create new graph:

  graph = Graph.new(edges)

By default graphs are implemented as adjacency lists. This implementation works in most situations. However, sometimes triangular matrix may be better choice for internal graph representation (for e.g. dense graphs). You can set graph internal representation by passing second argument to initializer or using special constructor.

  graph = Graph.new_dense(edges)

or

  graph = Graph.new(edges, :tri_matrix)

Graph API

Some methods defined on graph object:

• degree
• edge?
• add_edge
• add_edges
• get_edge
• vertex_size
• remove
• add
• neighbors
• vertexes
• edges

Examples:

  graph.vertex_size #=> 4
  graph.degree("Bob") #=> 3
  graph.edge?("Bob", "Tom") #=> true
  graph.edge?("Tom", "Jack") #=> false
  graph.add_edge(Edge.new("Bob", "Kate"))
  graph.remove("Bob", "Jack")
  graph.neighbors('Tom') #=> ["Bob", "Jim"]
  graph.add("Bob", "Jack")

Iterators:

  graph.each_edge { |e| p e }
  graph.each_vertex { |v| p v }

Digraph

Digraph (Directed Graph) is graph with directed edges.

Creating new directed graph (implemented as adjacency list):

  edges = []
  edges << Edge.new(:A, :C, 5)
  edges << Edge.new(:A, :D, 3)
  edges << Edge.new(:A, :G, 14)
  edges << Edge.new(:C, :E, 3)
  edges << Edge.new(:C, :F, 2)
  edges << Edge.new(:D, :C, 11)
  edges << Edge.new(:D, :E, 7)
  edges << Edge.new(:D, :G, 6)
  edges << Edge.new(:G, :E, 7)
  edges << Edge.new(:E, :B, 5)
  edges << Edge.new(:G, :B, 6)
  edges << Edge.new(:F, :B, 7)

  digraph = Digraph.new(edges)

New directed dense graph (implemented as matrix):

  digraph = Digraph.new_dense(edges)

or

  digraph = Digraph.new(edges, :matrix)

Digraph API

Digraph inherits from Graph so all methods defined in Graph are available. Digraph defines some additional methods specific to directed graphs:

• in_degree
• out_degree

Examples

  digraph.get_edge(:D, :C).weight #=> 11
  digraph.degree(:E) #=> 4
  digraph.in_degree(:E) #=> 3
  digraph.out_degree(:E) #=> 1

Searching

Breadth First Search:

  BreadthFirstSearch.new(digraph).search(:A) #=> [:A, :C, :D, :G, :E, :F, :B]

Depth First Search:

  DepthFirstSearch.new(digraph).search(:A) #=> [:A, :G, :B, :E, :D, :C, :F]

You can also pass block to search methods:

  DepthFirstSearch.new(digraph).search(:A) { |v| v.to_s.downcase }

If source vertex is not given, search method iterates over all vertexes in graph.

Topological Sort

Topological Sort sorts vertexes in topological order (all edges in graph points in the same direction). Works only for digraphs without cycles (Directed Acyclic Graphs)

  TopologicalSort.new(graph).sort #=> array of vertexes in topological order

Connected Compontents

ConnectedComponents finds all connected components in graph.

  cc = ConnectedComponents.new(graph)
  cc.count # => 1
  cc.connected?(:a, :b) # => true

Minimum Spanning Tree

MinimumSpanningTree finds tree connecting all vertexes in graph with minimal weights. Implements Kruskal's algorithm.

  tree = MinimumSpanningTree.new(graph).calculate #=> array of edges

Shortest Paths

Finds shortest paths from source to all vertexes in graph. Implements Dijkstra's algorithm and works only for digraphs with positive weights.

Finding shortest paths in graph from vertex 0:

  sp = ShortestPaths.new(digraph, 0)
  sp.distance_to(7) #=>  returns shortest distance from vertex 0 to vertex 7
  sp.has_path?(7) #=>  returns true if shortest path to 7 exists
  sp.path_to(4) #=>  returns path from vertex 0 to vertex 4 (array of vertexes)