1NAUTY-COUNTG(1) Nauty Manual NAUTY-COUNTG(1)
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6 nauty-countg - count graphs according to a variety of properties
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9 [pickg|countg] [-fp#:#q -V -X] [--keys] [-constraints -v] [ifile
10 [ofile]]
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13 countg : Count graphs according to their properties.
14 pickg : Select graphs according to their properties.
16 ifile, ofile : Input and output files.
18 '-' and missing names imply stdin and stdout.
20 Miscellaneous switches:
22 -p# -p#:#
24 Specify range of input lines (first is 1) May fail if input is
25 incremental.
26 -f With -p, assume input lines of fixed length (only used with a
28 file in graph6/digraph6 format)
29 -v Negate all constraints (but not -p)
31 -X Reverse selection (but -p still observed)
33 -V List properties of every input matching constraints.
35 -l Put a blank line whenever the first parameter changes, if there
37 are at least two parameters.
38 -1 Write output as lines of numbers separated by spaces, with 0/1
40 for boolean and both endpoints of ranges given separately even
41 if they are the same, and the count at the end of the line.
42 Also, no total is written.
43 -2 The same as -1 but counts are not written.
45 -q Suppress informative output.
47 Constraints:
49 Numerical constraints (shown here with following #) can take a
51 single integer value, or a range like #:#, #:, or :#. Each can
52 also be preceded by '~', which negates it. (For example,
53 -~D2:4 will match any maximum degree which is _not_ 2, 3, or 4.)
54 Constraints are applied to all input graphs, and only those
55 which match all constraints are counted or selected.
56 -n# number of vertices -e# number of edges
58 -ee# number of non-edges (including loops for digraphs)
60 -L# number of loops -C strongly connected
62 -LL# number of 2-cycles -cc# number of components
64 -d# minimum (out-)degree -D# maximum (out-)degree
66 -m# vertices of min (out-)degree -M# vertices of max (out-)degree
68 -u# minimum (in-)degree -U# maximum (in-)degree
70 -s# vertices of min (in-)degree -S# vertices of max (in-)degree
72 -r regular -b bipartite
74 -z# radius -Z# diameter
76 -g# girth (0=acyclic) -Y# total number of cycles
78 -h# maximum independent set -k# maximum clique
80 -T# number of triangles -K# number of maximal cliques
82 -TT# number independent sets of size 3
84 -B# smallest possible first side of a bipartition (0 if nonbipar‐
86 tite)
87 -H# number of induced cycles -W# number of 4-cycles
89 -E Eulerian (all degrees are even, connectivity not required)
91 -a# group size -o# orbits -F# fixed points -t vertex-transitive
93 -c# connectivity (only implemented for 0,1,2).
95 -i# min common nbrs of adjacent vertices; -I# maximum
97 -j# min common nbrs of non-adjacent vertices; -J# maximum
99 -x# number of sources -xx# number of sinks
101 -WW# number of diamonds
103 Sort keys:
105 Counts are made for all graphs passing the constraints.
107 Counts
108 are given separately for each combination of values occurring
110 for the properties listed as sort keys. A sort key is intro‐
111 duced by '--' and uses one of the letters known as constraints.
112 These can be combined: --n --e --r is the same as --ne --r
113 and --ner. The order of sort keys is significant. A comma can
114 be used as a separator.
115 The sort key ':' has a special purpose: the values of sort keys
117 following ':' are given as ranges rather than creating a sepa‐
118 rate line for each value. For example --e:zZ will give the
119 ranges of radius and diameter that occur for each number of
120 edges. The output format matches the input, except that sparse6
121 is used to output an incremental graph whose predecessor is not
122 output.
123nauty 2.8.6 September 2023 NAUTY-COUNTG(1)