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.
ftM2int(ft) int2ftM(i)
i |
Numeric vector. |
ft |
Numeric nx2 or 2xn matrix. |
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.
For ftM2int, a numeric vector of length n.
For int2ftM, a length(i) x 2 matrix.
Wolfgang Huber
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))
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