2024/05/25 by Michael Maxfield, Jingcheng Xu, Maxfield, Michael +3 · 1 citation
Business, Management and Accounting · Computer Science · Physics and Astronomy · #Advanced Queuing Theory Analysis #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Biological sciences #FOS: Mathematics #Interconnection Networks and Systems #Populations and Evolution (q-bio.PE)
paper · pdf · doi:10.48550/arxiv.2405.16035
openalex publication_date 2024/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Semidirected networks have received interest in evolutionary biology as the appropriate generalization of unrooted trees to networks, in which some but not all edges are directed. Yet these networks lack proper theoretical study. We define here a general class of semidirected phylogenetic networks, with a stable set of leaves, tree nodes and hybrid nodes. We prove that for these networks, if we locally choose the direction of one edge, then globally the set of directed paths starting by this edge is stable across all choices to root the network. We define an edge-based representation of semidirected phylogenetic networks and use it to define a dissimilarity between networks, which can be efficiently computed in near-quadratic time. Our dissimilarity extends the widely-used Robinson-Foulds distance on both rooted trees and unrooted trees. After generalizing the notion of tree-child networks to semidirected networks, we prove that our edge-based dissimilarity is in fact a distance on the space of tree-child semidirected phylogenetic networks.