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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

Graph Representation


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


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


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 and test/ for how to do this.


digraphtools was initially written by David Basden


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

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