graph (version 1.50.0)

Standard labeling of edges with integers: Standard labeling of edges with integers

Description

Functions to convert between from-to representation and standard labeling of the edges for undirected graphs with no self-loops.

Usage

ftM2int(ft)
int2ftM(i)

Arguments

i

Numeric vector.

ft

Numeric nx2 or 2xn matrix.

Value

For ftM2int, a numeric vector of length n. For int2ftM, a length(i) x 2 matrix.

Details

A standard 1-based node labeling of a graph G=(V,E) is a one-to-one mapping between the integers from 1 to |V| and the nodes in V. A standard 1-based edge labeling of an undirected graph G=(V,E) with no self-loops is the one-to-one mapping between the integers from 1 to |V| choose 2 = |V|*(|V|-1)/2 such that the edge labeled 1 is between nodes 2 and 1, the edge labeled 2 is between nodes 3 and 1, the edge labeled 3 is between nodes 3 and 2, and so on.

Examples

 nNodes <- 200
 nEdges <- choose(nNodes, 2)
 i <- 1:nEdges
 ft <- int2ftM(i)
 ft[1:6,]
 stopifnot(all(ft[,1]>ft[,2])) ## always from higher to lower
 stopifnot(!any(duplicated(paste(ft[,1], ft[,2]))))
 stopifnot(ft[nEdges, 1]==nNodes, ft[nEdges, 2]==nNodes-1) 

 j <- ftM2int(ft)
 stopifnot(all(i==j))