How far is my network from being edge-based? Proximity measures for edge-basedness of unrooted phylogenetic networks

Mareike Fischer, Tom Niklas Hamann, Kristina Wicke

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Phylogenetic networks which are, as opposed to trees, suitable to describe processes like hybridization and horizontal gene transfer, play a substantial role in evolutionary research. However, while non-treelike events need to be taken into account, they are relatively rare, which implies that biologically relevant networks are often assumed to be similar to trees in the sense that they can be obtained by taking a tree and adding some additional edges. This observation led to the concept of so-called tree-based networks, which recently gained substantial interest in the literature. Unfortunately, though, identifying such networks in the unrooted case is an NP-complete problem. Therefore, classes of networks for which tree-basedness can be guaranteed are of the utmost interest. The most prominent such class is formed by so-called edge-based networks, which have a close relationship to generalized series–parallel graphs known from graph theory. They can be identified in linear time and are in some regards biologically more plausible than general tree-based networks. While concerning the latter proximity measures for general networks have already been introduced, such measures are not yet available for edge-basedness. This means that for an arbitrary unrooted network, the “distance” to the nearest edge-based network could so far not be determined. The present manuscript fills this gap by introducing two classes of proximity measures for edge-basedness, one based on the given network itself and one based on its so-called leaf shrink graph (LS graph). Both classes contain four different proximity measures, whose similarities and differences we study subsequently.

Original languageEnglish (US)
Pages (from-to)303-320
Number of pages18
JournalDiscrete Applied Mathematics
StatePublished - Oct 15 2023

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


  • Edge-based network
  • GSP graph
  • K-minor free graph
  • Phylogenetic network
  • Tree-based network


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