gRbase (version 1.7-5)

mcs: Maximum cardinality search on undirected graph.

Description

Returns (if it exists) a perfect ordering of the vertices in an undirected graph.

Usage

mcs(object, root = NULL, index = FALSE)
"mcs"(object, root = NULL, index = FALSE)

mcsMAT(amat, vn = colnames(amat), root = NULL, index = FALSE)
mcsmarked(object, discrete = NULL, index = FALSE)
"mcsmarked"(object, discrete = NULL, index = FALSE)

mcsmarkedMAT(amat, vn = colnames(amat), discrete = NULL, index = FALSE)

Arguments

object

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

root

A vector of variables. The first variable in the perfect ordering will be the first variable on 'root'. The ordering of the variables given in 'root' will be followed as far as possible.

discrete

A vector indicating which of the nodes are discrete. See 'details' for more information.

index

If TRUE, then a permutation is returned

amat

Adjacency matrix

vn

Nodes in the graph given by adjacency matrix

Value

A vector with a linear ordering (obtained by maximum cardinality search) of the variables or character(0) if such an ordering can not be created.

Details

An undirected graph is decomposable iff there exists a perfect ordering of the vertices. The maximum cardinality search algorithm returns a perfect ordering of the vertices if it exists and hence this algorithm provides a check for decomposability. The mcs() functions finds such an ordering if it exists.

The notion of strong decomposability is used in connection with e.g. mixed interaction models where some vertices represent discrete variables and some represent continuous variables. Such graphs are said to be marked. The mcsmarked() function will return a perfect ordering iff the graph is strongly decomposable. As graphs do not know about whether vertices represent discrete or continuous variables, this information is supplied in the discrete argument.

See Also

moralize jTree rip ug, dag

Examples

uG <- ug(~me+ve,~me+al,~ve+al,~al+an,~al+st,~an+st)
mcs(uG)
mcsMAT( graphNEL2M(uG) )
## Same as
uG <- ug(~me+ve,~me+al,~ve+al,~al+an,~al+st,~an+st,result="matrix")
mcsMAT(uG)

## Marked graphs
uG1 <- ug(~a:b+b:c+c:d)
uG2 <- ug(~a:b+a:d+c:d)
## Not strongly decomposable:
mcsmarked(uG1, discrete=c("a","d"))
## Strongly decomposable:
mcsmarked(uG2, discrete=c("a","d"))