nautycountg(1)
count graphs according to a variety of properties
SYNOPSIS
[pickgcountg]
[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 vertextransitive
 c#

connectivity (only implemented for 0,1,2).
 i#

min common nbrs of adjacent vertices; I# maximum
 j#

min common nbrs of nonadjacent 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.