Editing Tree (graph theory) (section)

===Polytree===
{{main|Polytree}}
A {{em|polytree}}<ref name="d99"/> (or ''directed tree''{{sfn|Deo|1974|p=206}} or ''oriented tree''<ref name="Harary 1980"/><ref name="s91"/> or ''singly connected network''<ref name="kp83"/>) is a [[directed acyclic graph]] (DAG) whose underlying undirected graph is a tree. In other words, if we replace its directed edges with undirected edges, we obtain an undirected graph that is both connected and acyclic.

Some authors restrict the phrase "directed tree" to the case where the edges are all directed towards a particular vertex, or all directed away from a particular vertex (see [[Arborescence (graph theory)|arborescence]]).<ref>{{cite journal
 | last = Chen | first = Wai-kai
 | doi = 10.1137/0114048
 | journal = [[SIAM Journal on Applied Mathematics]]
 | mr = 209064
 | pages = 550–560
 | title = On directed trees and directed {{mvar|k}}-trees of a digraph and their generation
 | volume = 14
 | year = 1966| issue = 3
 }}</ref><ref name=kozlov>{{cite journal
 | last = Kozlov | first = Dmitry N.
 | doi = 10.1006/jcta.1999.2984
 | issue = 1
 | journal = Journal of Combinatorial Theory
 | mr = 1713484
 | pages = 112–122
 | series = Series A
 | title = Complexes of directed trees
 | volume = 88
 | year = 1999}}</ref><ref>{{citation
 | last1 = Tran | first1 = Ngoc Mai
 | last2 = Buck | first2 = Johannes
 | last3 = Klüppelberg | first3 = Claudia
 | arxiv = 2102.06197
 | date = February 2024
 | doi = 10.1093/jrsssb/qkad165
 | journal = Journal of the Royal Statistical Society Series B: Statistical Methodology
 | title = Estimating a directed tree for extremes| volume = 86
 | issue = 3
 | pages = 771–792
 }}</ref>