# essentialGraph: Construct the essential graph In abn: Modelling Multivariate Data with Additive Bayesian Networks

 essentialGraph R Documentation

## Construct the essential graph

### Description

Constructs different versions of the essential graph from a given DAG

### Usage

```essentialGraph(dag, node.names = NULL, PDAG = "minimal")
```

### Arguments

 `dag` a matrix or a formula statement (see ‘Details’ for format) defining the network structure, a directed acyclic graph (DAG). `node.names` a vector of names if the DAG is given via formula, see ‘Details’. `PDAG` a character value that can be: minimal or complete, see ‘Details’.

### Details

This function returns an essential graph from a DAG, aka acyclic partially directed graph (PDAG). This can be useful if the learning procedure is defined up to a Markov class of equivalence. A minimal PDAG is defined as only directed edges are those who participate in v-structure. Whereas the completed PDAG: every directed edge corresponds to a compelled edge, and every undirected edge corresponds to a reversible edge.

The `dag` can be provided using a formula statement (similar to glm). A typical formula is ` ~ node1|parent1:parent2 + node2:node3|parent3`. The formula statement have to start with `~`. In this example, node1 has two parents (parent1 and parent2). node2 and node3 have the same parent3. The parents names have to exactly match those given in `node.names`. `:` is the separator between either children or parents, `|` separates children (left side) and parents (right side), `+` separates terms, `.` replaces all the variables in `node.names`.

### Value

A matrix giving the PDAG.

Gilles Kratzer

### References

West, D. B. (2001). Introduction to Graph Theory. Vol. 2. Upper Saddle River: Prentice Hall.

Chickering, D. M. (2013) A Transformational Characterization of Equivalent Bayesian Network Structures, arXiv:1302.4938.

Further information about abn can be found at:
http://r-bayesian-networks.org

### Examples

```dag <- matrix(c(0,0,0, 1,0,0, 1,1,0), nrow = 3, ncol = 3)
dist <- list(a="gaussian", b="gaussian", c="gaussian")
colnames(dag) <- rownames(dag) <- names(dist)

essentialGraph(dag)
```

abn documentation built on April 25, 2022, 9:06 a.m.