graph enumeration {bnlearn}

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)

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.

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.

Value

count.graphs() returns an objects of class bigz from the gmp package, a vector with the graph counts.

Author(s)

Marco Scutari

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

## Not run: 
count.graphs("dags.with.r.arcs", nodes = 3:6, r = 2)

## End(Not run)