cycles.py | ||

README.md |

## 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

```
echo "0 1\n0 2\n1 0\n1 3\n2 0\n3 0\n3 1\n3 2" | python cycles.py 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' graph.dot | wc -l
sed -n -e 's/^\s*\([0-9]\) -> \([0-9]\);$/\1 \2/p' graph.dot
```

The above lines work on DOT files like the following:

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

They would produce the following output:

```
3
0 1
0 2
1 0
2 0
2 1
```