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Topiary provides functions for Directed Graphs and Directed Acyclic Graphs (DAGs) in Ruby (1.9 and up):

  • Topological sort using Kahn's Algorithm, which is linear on the number of nodes.
  • Automatically create all digraphs or DAGs with V vertices.
  • See if two graphs are topologically distinct.
  • Filter a list of graphs to just the topologically distinct ones.

Topologically distinct directed acyclic graphs with four vertices


Topological Sort

First create some nodes as Topiary::Node objects, including a custom data attribute on each node if you want. Set up edges by calling n1.feeds! n2 or n2.needs! n1. Then when you're ready, pass a list of all the nodes to Topiary.sort. You'll get back an array containing every node in topological order. If you have any questions about using it, take a look at the tests.


If you don't like keeping your nodes in a plain array, you can create Graph objects, passing the nodes (or adding them later), and defining edges:

g =
n1 = "n1"
n2 = "n2"
g.add_edge! n1, n2

Getting all topologically distinct DAGs with V vertices and E edges

    select{|g| g.edges.count == 4}

You can also construct the nodes on your own and call acyclic_from_node_list instead.

If you don't mind cycles, you can use all_from_node_count and all_from_node_list.


There are lots of RSpec tests. Say rake to run them plus Rubocop, or rspec spec to run just the tests.

For sorting I tried to test all possible DAGs up to four nodes, although since I couldn't find a comprehensive list I just did my best with toothpicks and marshmallows. If you find that I skipped something, let me know! Anyway, after all these marshmallows I'm pretty sure the sort works. :-)

Contributing to topiary

  • Check out the latest master to make sure the feature hasn't been implemented or the bug hasn't been fixed yet.
  • Check out the issue tracker to make sure someone hasn't already requested and/or contributed it.
  • Fork the project.
  • Start a feature/bugfix branch.
  • Commit and push until you are happy with your contribution.
  • Make be sure to add tests for it. This is important so I don't break it in a future version unintentionally.
  • Please try not to mess with the Rakefile, version, or history. If you want to have your own version, that is fine, but please isolate that change to its own commit so I can cherry-pick around it.

Commands for building/releasing/installing:

  • rake build
  • rake install
  • rake release


Copyright (c) 2018 Paul A. Jungwirth. See LICENSE.txt for further details.


Topological sort for a Directed Acyclic Graph, in Ruby







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