# graph-mcs: Maximum cardinality search on undirected graph. In gRbase: A Package for Graphical Modelling in R

 graph-mcs R Documentation

## 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)

## Default S3 method:
mcs(object, root = NULL, index = FALSE)

mcsMAT(amat, vn = colnames(amat), root = NULL, index = FALSE)

mcs_marked(object, discrete = NULL, index = FALSE)

## Default S3 method:
mcs_marked(object, discrete = NULL, index = FALSE)

mcs_markedMAT(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. `index` If TRUE, then a permutation is returned `amat` Adjacency matrix `vn` Nodes in the graph given by adjacency matrix `discrete` A vector indicating which of the nodes are discrete. See 'details' for more information.

### 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
\code{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 \code{discrete} argument.
```

### 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.

### Note

The workhorse is the `mcsMAT` function.

### Author(s)

Søren Højsgaard, sorenh@math.aau.dk

`moralize`, `junction_tree`, `rip`, `ug`, `dag`

### Examples

``````
uG <- ug(~ me:ve + me:al + ve:al + al:an + al:st + an:st)
mcs(uG)
mcsMAT(as(uG, "matrix"))
## 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:
mcs_marked(uG1, discrete=c("a","d"))
## Strongly decomposable:
mcs_marked(uG2, discrete=c("a","d"))

``````

gRbase documentation built on Sept. 22, 2023, 5:12 p.m.