Some tools for working with digraphs, partial orders and topological sorting with Python

## Project description

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: [] }

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

## Project details

This version 0.2.1 0.2.0 0.1.0