============
digraphtools
============

Some tools for working with directed acyclic graphs, partial orders and 
topological sorting with Python

digraphtools was written as a lightweight way of using DAGs and partial
ordering to represent, sort and traverse dependency trees in a lightweight
way.

The code is hosted on github at https://github.com/dbasden/python-digraphtools

Graph Representation
====================

Graphs
------

A graph is represented as a dict which maps a node to a list
nodes connected via the outgoing edges of that node. 

e.g.

        graph = { 1: [2,3],
                  2: [3],
                  3: [] }

is a DAG represented by the edges  (1,2) (1,3) (2,3)
where the edge 2tuple is in the form of (from,to)

There are helper methods in deptools to generate graphs from a
list of edges, and vice versa

Binary relations
----------------

If a DAG represents dependencies, e.g. the edge (1,2) is taken
to mean "1 depends on 2", this is backwards from a binary relation.
(1,2) would be the relation 2P1


Topological Sorting
===================

There are two ways of generating linear extensions / topological sorts of
dependencies (i.e. orders items must be processed in to satisfy dependency 
requirements):

deptools.dfs_topsort_traversal
------------------------------

deptools.dfs_topsort_traversal will take a graph and iterate over a
single valid topologicaly sorted order

deptools.topsort.vr_topsort
---------------------------

deptools.topsort.vr_topsort will generate all valid linear extensions /
topological orderings given an initial 'seed' linear extension (such as
the one generated by deptools.dfs_topsort_traversal).  

The method does not take the graph format as used by deptools as input, 
but it does have a helper method to generate it's input matrix from a 
partial order set (which can be generated from a graph using helpers in 
deptools).

See the examples in topsort.py and test/test_topsort.py for how to do this.


Authors
=======

digraphtools was initially written by David Basden


Thanks
======

Thanks to Yaakov L. Varol and Doron Rotem for the design of the algorithm 
in topsort.py