Finding all the elementary circuits of a directed graph

Algorithm by D. B. Johnson

[1] Finding all the elementary circuits of a directed graph.
D. B. Johnson, SIAM Journal on Computing 4, no. 1, 77-84, 1975.
http://dx.doi.org/10.1137/0204007

Using the networkx package and a modified version of its simple_cycles() function. The algorithm was adapted so that it would not arbitrarily order vertices. Three lines now contain a sorted() statement.

Usage

python cycles.py 4 0,1 0,2 1,0 1,3 2,0 3,0 3,1 3,2

First argument is the number of vertices. Subsequent arguments are ordered pairs of comma separated vertices that make up the directed edges of the graph.

DOT file input

For simplicity, there is no DOT file parser included but the following allows to create a suitable argument string for simple DOT graphs.

Given a DOT file of a simple (no labels, colors, styles, only pairs of vertices...) directed graph, the following line produces commandline arguments in the above format for that graph.

echo `sed -n -e '/^\s*[0-9]\+;$/p' graph.dot | wc -l` `sed -n -e 's/^\s*\([0-9]\) -> \([0-9]\);$/\1,\2/p' graph.dot`

The above line works on DOT files like the following:

digraph G {
  0;
  1;
  2;
  0 -> 1;
  0 -> 2;
  1 -> 0;
  2 -> 0;
  2 -> 1;
  }

It would produce the following output:

3 0,1 0,2 1,0 2,0 2,1