graph-gcproperties: Properties of a generating class (for defining a graph).

In hojsgaard/gRbase: A Package for Graphical Modelling in R

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.

Value

TRUE or FALSE

Author(s)

Søren Højsgaard, [e-mail]

See Also

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 )

hojsgaard/gRbase documentation built on Jan. 10, 2024, 9:40 p.m.