NAME

       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 (but not -p)

       -X     Reverse selection (but -p still observed)

       -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.

       -1     Write output as lines of numbers separated by spaces, with 0/1 for boolean and both
              endpoints of ranges given separately even if they are the same, and  the  count  at
              the end of the line. Also, no total is written.

       -2     The same as -1 but counts are not written.

       -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

       -ee# number of non-edges (including loops for digraphs)

       -L#    number of loops              -C   strongly connected

       -LL# number of 2-cycles           -cc# number of components

       -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 (in-)degree  -S#  vertices of max (in-)degree

       -r     regular                      -b   bipartite

       -z#    radius                       -Z#  diameter

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

       -h#    maximum independent set      -k#  maximum clique

       -T#    number of triangles          -K#  number of maximal cliques

       -TT# number independent sets of size 3

       -B#    smallest possible first side of a bipartition (0 if nonbipartite)

       -H#    number of induced cycles     -W#  number of 4-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

       -x#    number of sources            -xx#  number of sinks

       -WW# number of diamonds

              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.  A comma can be  used  as  a
              separator.

              The  sort  key ':' has a special purpose: the values of sort keys following ':' are
              given as ranges rather than creating a separate line for each  value.  For  example
              --e:zZ  will  give  the ranges of radius and diameter that occur for each number of
              edges.  The output format matches the input, except that sparse6 is used to  output
              an incremental graph whose predecessor is not output.