# count.graphs: Count graphs with specific characteristics In bnlearn: Bayesian Network Structure Learning, Parameter Learning and Inference

## Description

Count directed acyclic graphs of various sizes with specific characteristics.

## Usage

 `1` ```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.

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

 ```1 2 3 4``` ```## Not run: count.graphs("dags.with.r.arcs", nodes = 3:6, r = 2) ## End(Not run) ```

bnlearn documentation built on Sept. 7, 2021, 1:07 a.m.