# mst

##### Minimum Spanning Tree

The function `mst`

finds the minimum spanning tree between a set of
observations using a matrix of pairwise distances.

The `plot`

method plots the minimum spanning tree showing the
links where the observations are identified by their numbers.

- Keywords
- multivariate

##### Usage

```
mst(X)
# S3 method for mst
plot(x, graph = "circle", x1 = NULL, x2 = NULL, …)
```

##### Arguments

- X
either a matrix that can be interpreted as a distance matrix, or an object of class

`"dist"`

.- x
an object of class

`"mst"`

(e.g. returned by`mst()`

).- graph
a character string indicating the type of graph to plot the minimum spanning tree; two choices are possible:

`"circle"`

where the observations are plotted regularly spaced on a circle, and`"nsca"`

where the two first axes of a non-symmetric correspondence analysis are used to plot the observations (see Details below). If both arguments`x1`

and`x2`

are given, the argument`graph`

is ignored.- x1
a numeric vector giving the coordinates of the observations on the

*x*-axis. Both`x1`

and`x2`

must be specified to be used.- x2
a numeric vector giving the coordinates of the observations on the

*y*-axis. Both`x1`

and`x2`

must be specified to be used.- …
further arguments to be passed to

`plot()`

.

##### Details

These functions provide two ways to plot the minimum spanning tree which
try to space as much as possible the observations in order to show as
clearly as possible the links. The option `graph = "circle"`

simply plots regularly the observations on a circle, whereas
`graph = "nsca"`

uses a non-symmetric correspondence analysis
where each observation is represented at the centroid of its neighbours.

Alternatively, the user may use any system of coordinates for the obsevations, for instance a principal components analysis (PCA) if the distances were computed from an original matrix of continous variables.

##### Value

an object of class `"mst"`

which is a square numeric matrix of size
equal to the number of observations with either `1`

if a link
between the corresponding observations was found, or `0`

otherwise. The names of the rows and columns of the distance matrix,
if available, are given as rownames and colnames to the returned object.

##### See Also

##### Examples

```
# NOT RUN {
require(stats)
X <- matrix(runif(200), 20, 10)
d <- dist(X)
PC <- prcomp(X)
M <- mst(d)
opar <- par()
par(mfcol = c(2, 2))
plot(M)
plot(M, graph = "nsca")
plot(M, x1 = PC$x[, 1], x2 = PC$x[, 2])
par(opar)
# }
```

*Documentation reproduced from package ape, version 5.3, License: GPL (>= 2)*