# mst: Minimum Spanning Tree In SyNet: Inference and Analysis of Sympatry Networks

## Description

Identifies the minimum spanning tree connecting the set of points using their spatial distances.

## Usage

 1 mst(x)

## Arguments

 x Distance matrix between points

## Details

Certainly, a single vector could be used to capture the topology of a MST, indicating the index of the parent node for each child node. However, I have decided to indicate the endpoints for each MST arc into two separate vectors.

## Value

This function returns a list with the following elements:

 path Length of the MST in the given metric units. wght Mean leangth of MST arcs incident to each vertex. Values are normalized so that they sum to unity. xy0 Indices for one of the endpoints of MST arcs. xy1 Indices for the other endpoints correspondingly ordered.

## Note

The algorithm to obtain the MST is valid for distance matrices with metric properties. Consequently, both Euclidean and orthodromic distances can be used.

## Author(s)

Daniel A. Dos Santos <dadossantos@csnat.unt.edu.ar>

## References

Prim R.C. 1957. Shortest Connecting Networks and Some Generalizations. Bell Syst. Tech. J 36:1389-1401.

## Examples

 1 2 3 4 xy <- matrix(rnorm(100), ncol = 2) # Sample a random set of points plot(xy, xlab = "", ylab = "", main = "MINIMUM SPANNING TREE") aux <- mst(as.matrix(dist(xy))) # Find the Euclidean minimum spanning tree segments(xy[aux\$xy0,1], xy[aux\$xy0,2], xy[aux\$xy1,1], xy[aux\$xy1,2]) # Plot the MST