# nauty-countg man page

nauty-countg — 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**# maximumSort 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.