graph-triangulate: Triangulation of an undirected graph

Description

This function will triangulate an undirected graph by adding fill-ins.

Usage

triangulate(object, ...)
# S3 method for default
triangulate(object, nLevels = NULL, result = NULL, check = TRUE, ...)
triang_mcwh(object, ...)
triang_elo(object, ...)
triang(object, ...)
# S3 method for default
triang(object, control = list(), ...)
# S3 method for default
triang_mcwh(object, nLevels = NULL, result = NULL, check = TRUE, ...)
# S3 method for default
triang_elo(object, order = NULL, result = NULL, check = TRUE, ...)
triangulateMAT(amat, nLevels = rep(2, ncol(amat)), ...)
triang_mcwhMAT_(amat, nLevels = rep(2, ncol(amat)), ...)
triang_eloMAT_(amat, order)
triang_eloMAT(amat, order = NULL)

Arguments

object

An undirected graph represented either as a graphNEL object, an igraph, a (dense) matrix, a (sparse) dgCMatrix.

...

Additional arguments, currently not used.

nLevels

The number of levels of the variables (nodes) when these are discrete. Used in determining the triangulation using a "minimum clique weight heuristic". See section 'details'.

result

The type (representation) of the result. Possible values are "graphNEL", "igraph", "matrix", "dgCMatrix". Default is the same as the type of object.

check

If TRUE (the default) it is checked whether the graph is triangulated before doing the triangulation; gives a speed up if FALSE

control

A list controlling the triangulation; see 'examples'.

order

Elimation order; a character vector or numeric vector.

amat

Adjacency matrix; a (dense) matrix, or a (sparse) dgCMatrix.

Value

A triangulated graph represented either as a graphNEL, a (dense) matrix or a (sparse) dgCMatrix.

Details

There are two type of functions: triang and triangulate

The workhorse is the triangulateMAT function.

The triangulation is made so as the total state space is kept low by applying a minimum clique weight heuristic: When a fill-in is necessary, the algorithm will search for an edge to add such that the complete set to be formed will have as small a state-space as possible. It is in this connection that the nLevels values are used.

Default (when nLevels=NULL) is to take nLevels=2 for all nodes. If nLevels is the same for all nodes then the heuristic aims at keeping the clique sizes small.

Examples

Run this code

# NOT RUN {
## graphNEL
uG1 <- ug(~a:b + b:c + c:d + d:e + e:f + f:a)
uG2 <- ug(~a:b + b:c + c:d + d:e + e:f + f:a, result="matrix")
uG3 <- ug(~a:b + b:c + c:d + d:e + e:f + f:a, result="dgCMatrix")

## Default triangulation: minimum clique weight heuristic
# (default is that each node is given the same weight):

tuG1 <- triang(uG1)
## Same as
triang_mcwh(uG1)

## Alternative: Triangulation from a desired elimination order
# (default is that the order is order of the nodes in the graph):

triang(uG1, control=list(method="elo"))
## Same as:
triang_elo(uG1)

## More control: Define the number of levels for each node:
tuG1 <- triang(uG1, control=list(method="mcwh", nLevels=c(2, 3, 2, 6, 4, 9))) 
tuG1 <- triang_mcwh(uG1, nLevels=c(2, 3, 2, 6, 4, 9))

tuG1 <- triang(uG1, control=list(method="elo", order=c("a", "e", "f")))
tuG1 <- triang_elo(uG1, order=c("a", "e", "f"))

## graphNEL
uG1 <- ug(~a:b + b:c + c:d + d:e + e:f + f:a)
tuG1 <- triangulate(uG1)

## adjacency matrix
uG2 <- ug(~a:b + b:c + c:d + d:e + e:f + f:a, result="matrix")
tuG2 <- triangulate(uG2)

## adjacency matrix (sparse)
uG2 <- ug(~a:b + b:c + c:d + d:e + e:f + f:a, result="dgCMatrix")
tuG2 <- triangulate(uG2)

# }

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