find all circuits of a directed graph using johnson's algorithm and ocaml implementation by pietro abate
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Finding all the elementary circuits of a directed graph

Algorithm by D. B. Johnson

Finding all the elementary circuits of a directed graph.
D. B. Johnson, SIAM Journal on Computing 4, no. 1, 77-84, 1975.

Functional and iterative version.

Additional code available at

Original git repository at

The original code was faulty. This version is fixed for the functional as well as the iterative version.


echo "0 1\n0 2\n1 0\n1 3\n2 0\n3 0\n3 1\n3 2" | ./cycles_{iter,functional}.native 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