Description Usage Arguments Details Value Author(s) References See Also Examples

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

1 | ```
findMST2.PPI(object, return.MST2only=TRUE)
``` |

`object` |
an object of class |

`return.MST2only` |
logical. If |

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.

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 |

`first.mst` |
an object of class |

`second.mst` |
an object of class |

Yasir Rahmatallah and Galina Glazko

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
## 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"
``` |

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