1NAUTY-WATERCLUSTER2(1)           Nauty Manual           NAUTY-WATERCLUSTER2(1)
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NAME

6       nauty-watercluster2  -  generate  small  digraphs with given underlying
7       graph (faster alternative to directg)
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SYNOPSIS

10       watercluster2 [ix] [oy] [S] [T] [B] [C] [m]
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DESCRIPTION

13              Reads graphs in g6 code or multicode (optional) from  stdin  and
14              directs them
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16              ix : the indegree of every vertex may be at most x.
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18              The default maximum indegree is unlimited.
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20              oy : the outdegree of every vertex may be at most y.
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22              The default maximum outdegree is unlimited.
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24              S : allow that for every pair of vertices x,y at most one of the
25              edges x-->y
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27              and y-->x may be present. By default both of them may be present
28              in the same graph.
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30              T  :  Output  directed  graphs in T-code. This is a simple ASCII
31              output format. Every line
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33              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
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38              B  :  Output the directed graphs in a binary code. Every item of
39              the code is an unsigned
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41              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.
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48              C  :  Do really construct all the directed graphs in memory, but
49              don't output them. This is not
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51              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.
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70              m : read multicode instead of g6 code
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72       This  program  uses  different  labelling  routines -- all based on the
73       ideas of
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75       G. Brinkmann, Generating water  clusters  and  other  directed  graphs,
76       Journal of Mathematical Chemistry 46, 1112--1121 (2009)
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80nauty 2.6.12                     January 2020           NAUTY-WATERCLUSTER2(1)
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