Recently, so-called tree-based phylogenetic networks have attracted considerable attention. These networks can be constructed from a phylogenetic tree, called the base tree, by adding additional edges. The primary aim of this study is to provide sufficient criteria for tree-basedness by reducing phylogenetic networks to related graph structures. Even though it is generally known that determining whether a network is tree-based is an NP-complete problem, one of these criteria, namely edge-basedness, can be verified in linear time. Surprisingly, the class of edge-based networks is closely related to a well-known family of graphs, namely, the class of generalized series-parallel graphs, and we explore this relationship in full detail. Additionally, we introduce further classes of tree-based networks and analyze their relationships.

中文翻译：

---

基于树的网络的类别。

近来，所谓的基于树的系统发育网络引起了相当大的关注。这些网络可以通过添加额外的边缘，从称为基础树的系统树中构建。这项研究的主要目的是通过将系统进化网络简化为相关的图结构，从而为基于树的行为提供足够的标准。尽管通常已知确定网络是否基于树是NP完全问题，但是可以在线性时间内验证这些标准之一，即基于边缘。出人意料的是，基于边缘的网络的类别与众所周知的图族（即广义的系列-平行图的类别）紧密相关，我们将详细探讨这种关系。此外，我们介绍了更多类的基于树的网络并分析了它们之间的关系。