NAUTY-COUNTG(1) Nauty Manual NAUTY-COUNTG(1) 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.-fWith-p, assume input lines of fixed length (only used with a file in graph6/digraph6 format)-vNegate all constraints-VList properties of every input matching constraints.-lPut a blank line whenever the first parameter changes, if there are at least two parameters.-qSuppress 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-Cstrongly 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-rregular-bbipartite-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-EEulerian (all degrees are even, connectivity not required)-a# group size-o# orbits-F# fixed points-tvertex-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 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 --ris the same as--ne --rand--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. nauty 2.6.12 October 2019 NAUTY-COUNTG(1)