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
k.a.hawick@massey.ac.nz; heath.james@sapac.edu.au
Tel: +64 9 414 0800
Fax: +64 9 441 8181
Technical Report CSTN-013

Usage

make
./circuits_hawick 4 0,1 0,2 1,0 1,3 2,0 3,0 3,1 3,2

First argument is the number of vertices. Subsequent arguments are ordered pairs of comma separated vertices that 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 for simple DOT graphs.

Given a DOT file of a simple (no labels, colors, styles, only pairs of vertices...) directed graph, the following line produces commandline arguments in the above format for that graph.

echo `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 line works on DOT files like the following:

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

It 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:

./circuits_hawick 16 0,2 0,10 0,14 1,5 1,8 2,7 2,9 3,3 3,4 3,6 4,5 4,13 \
4,15 6,13 8,0 8,4 8,8 9,9 10,7 10,11 11,6 12,1 12,1 12,2 12,10 12,12 \
12,14 13,3 13,12 13,15 14,11 15,0