# ewLasso

##### Incomplete distances and edge weights of unrooted topology

This function implements a method for checking whether an incomplete set of distances satisfy certain conditions that might make it uniquely determine the edge weights of a given topology, T. It prints information about whether the graph with vertex set the set of leaves, denoted by X, and edge set the set of non-missing distance pairs, denoted by L, is connected or strongly non-bipartite. It then also checks whether L is a triplet cover for T.

- Keywords
- multivariate

##### Usage

`ewLasso(X, phy)`

##### Arguments

- X
a distance matrix.

- phy
an unrooted tree of class

`"phylo"`

.

##### Details

Missing values must be represented by either `NA`

or a negative value.

This implements a method for checking whether an incomplete set of distances satisfies certain conditions that might make it uniquely determine the edge weights of a given topology, T. It prints information about whether the graph, G, with vertex set the set of leaves, denoted by X, and edge set the set of non-missing distance pairs, denoted by L, is connected or strongly non-bipartite. It also checks whether L is a triplet cover for T. If G is not connected, then T does not need to be the only topology satisfying the input incomplete distances. If G is not strongly non-bipartite then the edge-weights of the edges of T are not the unique ones for which the input distance is satisfied. If L is a triplet cover, then the input distance matrix uniquely determines the edge weights of T. See Dress et al. (2012) for details.

##### Value

NULL, the results are printed in the console.

##### References

Dress, A. W. M., Huber, K. T., and Steel, M. (2012) `Lassoing' a
phylogentic tree I: basic properties, shellings and covers.
*Journal of Mathematical Biology*, **65(1)**, 77--105.

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