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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.

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.


echo "0 1\n0 2\n1 0\n1 3\n2 0\n3 0\n3 1\n3 2" | python 4

First argument is the number of vertices. Ordered pairs of space separated vertices are given via standard input and 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 and standard input for simple DOT graphs.

Given a DOT file of a simple (no labels, colors, styles, only pairs of vertices...) directed graph, the following lines generate the number of vertices as well as the edge list expected on standard input.

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

The above lines work on DOT files like the following:

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

They would produce the following output:

0 1
0 2
1 0
2 0
2 1
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