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

Description Usage Arguments Details Value Note Author(s) References Examples

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

  mst(x)

`x`	Distance matrix between points

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.

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.

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

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

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

  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

Loading required package: tkrplot
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Warning messages:
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