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.
- -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
- 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.