# graph-gcproperties: Properties of a generating class (for defining a graph). In gRbase: A Package for Graphical Modelling in R

 graph-gcproperties R Documentation

## Properties of a generating class (for defining a graph).

### Description

A set of generators define an undirected graph, here called a dependence graph. Given a set of generators it is checked 1) if the dependence dependence graph is in 1-1-correspondance with the genrators (such that the corresponding model is graphical) and 2) if the dependence graph is chordal (triangulated) (such that the corresponding model is decomposable).

### Usage

```isGraphical(x)

isDecomposable(x)
```

### Arguments

 `x` A generating class given as right hand sided formula or a list; see `examples` below.

### Details

A set of sets of variables, say A_1, A_2, ... A_K is called a generating class for a graph with vertices V and edges E. If two variables a,b are in the same generator, say A_j, then a and b are vertices in the graph and there is an undirected edge between a and b.

```The graph induced by \code{g1 = ~a:b + a:c + b:c + c:d} has
edges \code{ab, ac, bc, cd}. The
cliques of this graph are \code{abc, cd}. Hence there is not a
1-1-correspondance between the graph and the generators.

On the other hand, \code{g2 <- ~a:b:c + c:d} induces the same
graph in this case there is a 1-1-correspondance.

The graph induced by \code{g3 <- ~a:b + b:c + c:d + d:a} is in
1-1-correspondance with its dependence graph, but the graph is
not chordal.
```

TRUE or FALSE

### Author(s)

Søren Højsgaard, sorenh@math.aau.dk

`mcs`, `rip`

### Examples

```
g1 <- ~a:b + a:c + b:c + c:d
g2 <- ~a:b:c + c:d
g3 <- ~a:b + b:c + c:d + d:a

isGraphical( g1 ) # FALSE
isGraphical( g2 ) # TRUE
isGraphical( g3 ) # TRUE

isDecomposable( g1 ) # FALSE
isDecomposable( g2 ) # TRUE
isDecomposable( g3 ) # TRUE

## A generating class can be given as a list:
f <- list(c("a","b"), c("b","c"), c("a","c"))
isGraphical( f )
isDecomposable( f )

```

gRbase documentation built on April 2, 2022, 5:06 p.m.