1NAUTY-WATERCLUSTER2(1) Nauty Manual NAUTY-WATERCLUSTER2(1)
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6 nauty-watercluster2 - generate small digraphs with given underlying
7 graph (faster alternative to directg)
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10 watercluster2 [ix] [oy] [S] [T] [B] [C] [m]
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13 Reads graphs in g6 code or multicode (optional) from stdin and
14 directs them
15 ix : the indegree of every vertex may be at most x.
17 The default maximum indegree is unlimited.
19 oy : the outdegree of every vertex may be at most y.
21 The default maximum outdegree is unlimited.
23 S : allow that for every pair of vertices x,y at most one of the
25 edges x-->y
26 and y-->x may be present. By default both of them may be present
28 in the same graph.
29 T : Output directed graphs in T-code. This is a simple ASCII
31 output format. Every line
32 contains one graph. First the number of vertices, then the num‐
34 ber of directed edges and then the list of directed edges with
35 the start first and the end then. E.g.: 3 2 0 1 2 1 means 3 ver‐
36 tices, 2 directed edges: 0-->1 and 2-->1
37 B : Output the directed graphs in a binary code. Every item of
39 the code is an unsigned
40 char. The first unsigned char is the number nv of vertices. The
42 vertices are numbered 1..nv Then the list of vertices x for
43 which there is a directed edge 1->x follow. This list is ended
44 by a 0. Then the list of outgoing neighbours of 2 follows --
45 again ended with a 0, etc. The code is complete with the 0 end‐
46 ing the list of outgoing neighbours of nv.
47 C : Do really construct all the directed graphs in memory, but
49 don't output them. This is not
50 a big difference in case of restricted in- and outdegrees,
52 because all that is done extra is that edges are directed
53 instead of just keeping track of in- and out-degrees. This
54 option is intended only for testing purposes to test also rou‐
55 tines that are normally not used when counting. Things that
56 would speed up the counting also in some cases of restricted in-
57 and out-degrees -- like multiplying the possibilities of assign‐
58 ing directions to edges that can be assigned directions indepen‐
59 dent of each other (depending on the degrees of the endvertices
60 and overlaps) -- are not included. In case of not restrictive
61 bounds on the in- and out-degree it not really constructing the
62 graphs can be considerably faster. In cases of restricted in-
63 and out-degrees the only difference is that the graph isn't mod‐
64 ified... The fact that in case of no output the graph is not
65 modified is mainly to save time for the one case of waterclus‐
66 ters, where large numbers were determined. If large numbers
67 (without output) for other cases shall be determined, one should
68 think about adding the multiplication routines.
69 m : read multicode instead of g6 code
71 This program uses different labelling routines -- all based on the
73 ideas of
74 G. Brinkmann, Generating water clusters and other directed graphs,
76 Journal of Mathematical Chemistry 46, 1112--1121 (2009)
77nauty 2.6.11 February 2019 NAUTY-WATERCLUSTER2(1)