nautycountg man page
nautycountg — 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.