Level-2 networks from shortest and longest distances

Journal article (2022)

Authors

Katharina T Huber University of East Anglia
L.J.J. van Iersel Discrete Mathematics and Optimization - EEMCS
R. Janssen Discrete Mathematics and Optimization - EEMCS
M.E.L. Jones Discrete Mathematics and Optimization - EEMCS
Vincent Moulton University of East Anglia
Yukihiro Murakami Discrete Mathematics and Optimization - EEMCS
Research Group
Discrete Mathematics and Optimization (EEMCS) (TU Delft)
Copyright: © 2022 Katharina T. Huber, L.J.J. van Iersel, R. Janssen, M.E.L. Jones, Vincent Moulton, Yukihiro Murakami
DOI: https://doi.org/10.1016/j.dam.2021.09.026
Phylogenetic networks Distance matrix Level-k network Reconstructibility
More Info
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Published Date

2022

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Discrete Mathematics and Optimization

Abstract

Recently it was shown that a certain class of phylogenetic networks, called level-2 networks, cannot be reconstructed from their associated distance matrices. In this paper, we show that they can be reconstructed from their induced shortest and longest distance matrices. That is, if two level-2 networks induce the same shortest and longest distance matrices, then they must be isomorphic. We further show that level-2 networks are reconstructible from their shortest distance matrices if and only if they do not contain a subgraph from a family of graphs. A generator of a network is the graph obtained by deleting all pendant subtrees and suppressing degree-2 vertices. We also show that networks with a leaf on every generator side are reconstructible from their induced shortest distance matrix.