s = buildGraphFilter h
s = buildGraphFilter l
The filterGraphs and countGraphs methods both can use a tremendous number of constraints which are described by a rather tersely encoded string. This method builds that string given information in the HashTable $h$ or the List $l$. Any keys which do not exist are simply ignored and any values which are not valid (e.g., exactly $3$ vertices) are also ignored.
The values can either be Boolean or in ZZ. Boolean values are treated exactly as expected. Numerical values are more complicated; we use an example to illustrate how numerical values can be used, but note that this usage works for all numerically valued keys.
The key NumEdges restricts to a specific number of edges in the graph. If the value is the integer $n$, then only graphs with exactly $n$ edges are returned.



If the value is the Sequence $(m,n)$, then all graphs with at least $m$ and at most $n$ edges are returned.


If the value is the Sequence $(,n)$, then all graphs with at most $n$ edges are returned.


If the value is the Sequence $(m,)$, then all graphs with at least $m$ edges are returned.


Moreover, the associated key NegateNumEdges, if true, causes the opposite to occur.


The following are the boolean options: "Regular", "Bipartite", "Eulerian", "VertexTransitive".
The following are the numerical options (recall all have the associate "Negate" option): "NumVertices", "NumEdges", "MinDegree", "MaxDegree", "Radius", "Diameter", "Girth", "NumCycles", "NumTriangles", "GroupSize", "Orbits", "FixedPoints", "Connectivity", "MinCommonNbrsAdj", "MaxCommonNbrsAdj", "MinCommonNbrsNonAdj", "MaxCommonNbrsNonAdj".
Connectivity only works for the values $0, 1, 2$ and uses the following definition of $k$connectivity. A graph is $k$connected if $k$ is the minimum size of a set of vertices whose complement is not connected.
Thus, in order to filter for connected graphs, one must use {"Connectivity" => 0, "NegateConnectivity" => true}.
NumCycles can only be used with graphs on at most $n$ vertices, where $n$ is the number of bits for which nauty was compiled, typically $32$ or $64$.
The object buildGraphFilter is a method function.