findMST2.PPI {GSAR} | R Documentation

## Union of the First and Second Minimum Spanning Trees for PPI Networks

### Description

Find the union of the first and second minimum spanning trees for protein-protein interaction (PPI) networks.

### Usage

    findMST2.PPI(object, return.MST2only=TRUE)

### Arguments

`object` | an object of class `igraph` representing the PPI network.
`return.MST2only` | logical. If `TRUE` (default), an object of class `igraph` containing the MST2 is returned. If `FALSE`, a list of length three containing objects of class `igraph` is returned. The first and second objects are the first and second MSTs, respectively. The third is the union of the first and second, MST2.

### Details

This function produces the union of the first and second minimum spanning trees (MSTs) as an `igraph` object (check package `igraph` for details). It can as well return the first and second minimum spanning trees when `return.MST2only` is `FALSE`.

For the graph G(V,E) where V is the set of vertices and E is the set of edges, the first MST is defined as the acyclic subset T_{1} \subseteq E that connects all vertices in V and whose total length ∑_{i,j \in T_{1}} d(v_{i},v_{j}) is minimal (Rahmatallah et. al. 2014). The second MST is defined as the MST of the reduced graph G(V,E-T_{1}). The union of the first and second MSTs is denoted as MST2.

It was shown in Zybailov et. al. 2016 that MST2 can be informative as a graphical visualization tool in deciphering the properties of protein-protein interaction (PPI) networks by highlighting the minimum set of essential interactions among proteins. Most influential proteins with many interactions tend to occupy central position and have relatively high connectivity degree in the MST2 because the shortest paths connecting the vertices of the first and second MSTs tend to pass through the verteces corresponding to these proteins. In contrast, proteins with few interactions most likely occupy non-central positions in the MST2 and have a degree of 2.

### Value

If `return.MST2only=TRUE` (default), function `findMST2.PPI` returns an object of class `igraph` representing the MST2. If `return.MST2only=FALSE`, function `findMST2.PPI` returns a list of length 3 with the following components:

`MST2` | an object of class `igraph` containing the union of the first and second MSTs.
`first.mst` | an object of class `igraph` containing the first MST.
`second.mst` | an object of class `igraph` containing the second MST.

### Author(s)

Yasir Rahmatallah and Galina Glazko

### References

Zybailov B., Byrd A., Glazko G., Rahmatallah Y. and Raney K. (2016) Protein-protein interaction analysis for functional characterization of helicases. Methods, 108, 56–64.

### See Also

`GSNCAtest`, `plotMST2.pathway`.

### Examples

    ## generate a random undirected graph with power-law
    ## distribution degree where minimum degree is 4 and
    ## maximum degree is 100
    set.seed(123)
    degs <- sample(c(4:100), 100, replace=TRUE, prob=c(4:100)^-2)
    if(floor(sum(degs)/2) != (sum(degs)/2)) degs[1] <- degs[1] + 1
    randomGraph <- sample_degseq(degs, method="vl")
    ## find MST2 of the random graph and highlight vertices
    ## with degree greater than 10 with red color
    mst2.ppi <- findMST2.PPI(object=randomGraph, return.MST2only=TRUE)
    degs <- degree(mst2.ppi)
    ind <- which(degs > 10)
    V(mst2.ppi)$color <- "yellow"
    V(mst2.ppi)$color[ind] <- "red"

[Package GSAR version 1.16.0 Index]