bnlearn (version 4.7.1)

graph enumeration: Count graphs with specific characteristics

Description

Count directed acyclic graphs of various sizes with specific characteristics.

Usage

count.graphs(type = "all.dags", nodes, ..., debug = FALSE)

Value

count.graphs() returns an objects of class bigz from the

gmp package, a vector with the graph counts.

Arguments

type

a character string, the label describing the types of graphs to be counted (see below).

nodes

a vector of positive integers, the graph sizes as given by the numbers of nodes.

...

additional parameters (see below).

debug

a boolean value. If TRUE a lot of debugging output is printed; otherwise the function is completely silent. Ignored in some generation methods.

Author

Marco Scutari

Details

The types of graphs, and the associated additional parameters, are:

• all-dags: all directed acyclic graphs.

• dags-given-ordering: all directed acyclic graphs with a specific topological ordering.

• dags-with-k-roots: all directed acyclic graphs with k root nodes.

• dags-with-r-arcs: all directed acyclic graphs with r arcs.

References

Harary F, Palmer EM (1973). "Graphical Enumeration". Academic Press.

Rodionov VI (1992). "On the Number of Labeled Acyclic Digraphs". Discrete Mathematics, 105:319--321.

Liskovets VA (1976). "On the Number of Maximal Vertices of a Random Acyclic Digraph". Theory of Probability and its Applications, 20(2):401--409.

Examples

if (FALSE) {
count.graphs("dags.with.r.arcs", nodes = 3:6, r = 2)
}