nauty-countg man page

nauty-countg — count graphs according to a variety of properties


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


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.


With -p, assume input lines of fixed length (only used with a file in graph6/digraph6 format)


Negate all constraints


List properties of every input matching constraints.


Put a blank line whenever the first parameter changes, if there are at least two parameters.


Suppress informative output.


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.


number of vertices           -e#  number of edges


number of loops              -C   strongly connected


minimum (out-)degree         -D#  maximum (out-)degree


vertices of min (out-)degree -M#  vertices of max (out-)degree


minimum (in-)degree          -U#  maximum (in-)degree


vertices of min (out-)degree -S#  vertices of max (out-)degree


regular                      -b   bipartite


radius                       -Z#  diameter


girth (0=acyclic)            -Y#  total number of cycles


number of triangles          -K#  number of maximal cliques


smallest side of some bipartition (0 if none)


number of induced cycles


Eulerian (all degrees are even, connectivity not required)


group size  -o# orbits  -F# fixed points  -t vertex-transitive


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


min common nbrs of adjacent vertices;     -I# maximum


min common nbrs of non-adjacent vertices; -J# maximum

Sort keys:

Counts are made for all graphs passing the constraints.


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.


July 2018 nauty 2.6.10 Nauty Manual