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Finding all the circuits of a directed graph with self-arcs and multiple-arcs

Algorithm and code by K.A. Hawick and H.A. James

Enumerating Circuits and Loops in Graphs with Self-Arcs and Multiple-Arcs
K.A. Hawick and H.A. James
Computer Science, Institute for Information and Mathematical Sciences,
Massey University, North Shore 102-904, Auckland, New Zealand
[email protected]; [email protected]
Tel: +64 9 414 0800
Fax: +64 9 441 8181
Technical Report CSTN-013

Usage

make
echo "0 1\n0 2\n1 0\n1 3\n2 0\n3 0\n3 1\n3 2" | ./circuits_hawick 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

Reproducing the example from the paper

Figure 10 of the paper cited above:

0  10  11  6  13   3  4  15  0                    1   8   4  13  12  1
0  10  11  6  13  12  1   8  0                    1   8   4  13  12  1
0  10  11  6  13  12  1   8  4  15  0             3   3
0  10  11  6  13  12  1   8  0                    3   4  13   3
0  10  11  6  13  12  1   8  4  15  0             3   6  13   3
0  10  11  6  13  15  0                           6  13  12  10  11  6
0  14  11  6  13   3  4  15  0                    6  13  12  14  11  6
0  14  11  6  13  12  1   8  0                    8   8
0  14  11  6  13  12  1   8  4  15  0             9   9
0  14  11  6  13  12  1   8  0                   12  12
0  14  11  6  13  12  1   8  4  15  0
0  14  11  6  13  15  0

Figure 10: 22 Circuits found in the network shown in figure 9 which has 16 nodes and 32 arcs and allows self-arcs. Note there are repeated circuits due to the presence of a multiple-arc connecting nodes 12 and 1.

The input graph, which is shown in figure 9, can be given as an input to the program using above format as follows:

echo "0 2\n0 10\n0 14\n1 5\n1 8\n2 7\n2 9\n3 3\n3 4\n3 6\n4 5\n4 13\n\
4 15\n6 13\n8 0\n8 4\n8 8\n9 9\n10 7\n10 11\n11 6\n12 1\n12 1\n12 2\n12 10\n12 12\n\
12 14\n13 3\n13 12\n13 15\n14 11\n15 0" | ./circuits_hawick 16