4 Incomplete distances and edge weights of unrooted topology
7 This function implements a method for checking whether an incomplete
8 set of distances satisfy certain conditions that might make it
9 uniquely determine the edge weights of a given topology, T. It prints
10 information about whether the graph with vertex set the set of leaves,
11 denoted by X, and edge set the set of non-missing distance pairs,
12 denoted by L, is connected or strongly non-bipartite. It then also
13 checks whether L is a triplet cover for T.
19 \item{X}{a distance matrix.}
20 \item{phy}{an unrooted tree of class \code{"phylo"}.}
23 Missing values must be represented by either \code{NA} or a negative value.
25 This implements a method for checking whether an incomplete set of
26 distances satisfies certain conditions that might make it uniquely
27 determine the edge weights of a given topology, T. It prints
28 information about whether the graph, G, with vertex set the set of
29 leaves, denoted by X, and edge set the set of non-missing distance
30 pairs, denoted by L, is connected or strongly non-bipartite. It also
31 checks whether L is a triplet cover for T. If G is not connected, then
32 T does not need to be the only topology satisfying the input
33 incomplete distances. If G is not strongly non-bipartite then the
34 edge-weights of the edges of T are not the unique ones for which the
35 input distance is satisfied. If L is a triplet cover, then the input
36 distance matrix uniquely determines the edge weights of T. See Dress
37 et al. (2012) for details.
40 NULL, the results are printed in the console.
43 Dress, A. W. M., Huber, K. T., and Steel, M. (2012) `Lassoing' a
44 phylogentic tree I: basic properties, shellings and covers.
45 \emph{Journal of Mathematical Biology}, \bold{65(1)}, 77--105.
47 \author{Andrei Popescu \email{niteloserpopescu@gmail.com}}
48 \keyword{multivariate}