# josch/cycles_johnson_networkx

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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.
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
``````
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