nauty-countg(1) count graphs according to a variety of properties

SYNOPSIS

[pickg|countg] [-fp#:#q -V] [--keys] [-constraints -v] [ifile [ofile]]

DESCRIPTION

countg : Count graphs according to their properties.
pickg : Select graphs according to their properties.
ifile, ofile : Input and output files.
'-' and missing names imply stdin and stdout.
Miscellaneous switches:
-p# -p#:#
Specify range of input lines (first is 1) May fail if input is incremental.
-f
With -p, assume input lines of fixed length (only used with a file in graph6/digraph6 format)
-v
Negate all constraints
-V
List properties of every input matching constraints.
-l
Put a blank line whenever the first parameter changes, if there are at least two parameters.
-q
Suppress informative output.
Constraints:
Numerical constraints (shown here with following #) can take a single integer value, or a range like #:#, #:, or :#. Each can also be preceded by '~', which negates it. (For example, -~D2:4 will match any maximum degree which is _not_ 2, 3, or 4.) Constraints are applied to all input graphs, and only those which match all constraints are counted or selected.
-n#
number of vertices -e# number of edges
-L#
number of loops -C strongly connected
-d#
minimum (out-)degree -D# maximum (out-)degree
-m#
vertices of min (out-)degree -M# vertices of max (out-)degree
-u#
minimum (in-)degree -U# maximum (in-)degree
-s#
vertices of min (out-)degree -S# vertices of max (out-)degree
-r
regular -b bipartite
-z#
radius -Z# diameter
-g#
girth (0=acyclic) -Y# total number of cycles
-T#
number of triangles -K# number of maximal cliques
-B#
smallest side of some bipartition (0 if none)
-H#
number of induced cycles
-E
Eulerian (all degrees are even, connectivity not required)
-a#
group size -o# orbits -F# fixed points -t vertex-transitive
-c#
connectivity (only implemented for 0,1,2).
-i#
min common nbrs of adjacent vertices; -I# maximum
-j#
min common nbrs of non-adjacent vertices; -J# maximum
Sort keys:
Counts are made for all graphs passing the constraints.
Counts
are given separately for each combination of values occurring for the properties listed as sort keys. A sort key is introduced by '--' and uses one of the letters known as constraints. These can be combined: --n --e --r is the same as --ne --r and --ner. The order of sort keys is significant.
The output format matches the input, except that sparse6 is used to output an incremental graph whose predecessor is not output.