# Standard labeling of edges with integers

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##### Standard labeling of edges with integers

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

Keywords
graphs
##### Usage
ftM2int(ft)
int2ftM(i)
##### Arguments
i
Numeric vector.
ft
Numeric nx2 or 2xn 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.

##### Value

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

• ftM2int
• int2ftM
##### 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))

Documentation reproduced from package graph, version 1.50.0, License: Artistic-2.0

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