Editing Hierarchy (section)

===Degree of branching <span id="Terminology"></span>===
[[Degree (graph theory)|Degree]] of [[Bifurcation theory|branching]] refers to the number of direct [[#Terminology|subordinates]] or children an object has (in graph theory, equivalent to the number of other [[vertex (graph theory)|vertices]] connected to via outgoing arcs, in a directed graph) a node has. Hierarchies can be categorized based on the "maximum degree", the highest degree present in the system as a whole. Categorization in this way yields two broad classes: ''linear'' and ''branching''.

In a '''linear hierarchy'''<!--per WP:R#PLA, this SHOULD be bold-->, the maximum degree is 1.<ref name="Dawkins"/> In other words, all of the objects can be visualized in a line-up, and each object (excluding the top and bottom ones) has exactly one direct subordinate and one direct superior. This is referring to the ''objects'' and not the ''levels''; every hierarchy has this property with respect to levels, but normally each level can have an infinite number of objects.

In a '''branching hierarchy'''<!--per WP:R#PLA, this SHOULD be bold-->, one or more objects has a degree of 2 or more (and therefore the minimum degree is 2 or higher).<ref name="Dawkins"/> For many people, the word "hierarchy" automatically evokes an image of a branching hierarchy.<ref name="Dawkins"/> Branching hierarchies are present within numerous systems, including [[organization]]s and [[classification scheme]]s. The broad category of branching hierarchies can be further subdivided based on the degree.

A '''flat hierarchy'''<!--per WP:R#PLA, this SHOULD be bold--> (also known for companies as [[flat organization]]) is a branching hierarchy in which the maximum degree approaches infinity, i.e., that has a wide span.<ref name="Architecture">{{cite journal|last=Simon|first=Herbert A.|title=The Architecture of Complexity|journal=[[Proceedings of the American Philosophical Society]]|volume=106|issue=6|date=12 December 1962|pages=467–482|publisher=[[American Philosophical Society]]|issn=0003-049X|location=Philadelphia, Pennsylvania |jstor=985254 |citeseerx=10.1.1.110.961}}{{registration required}}</ref> Most often, systems intuitively regarded as hierarchical have at most a moderate span. Therefore, a flat hierarchy is often not viewed as a hierarchy at all. For example, [[diamond]]s and [[graphite]] are flat hierarchies of numerous [[carbon]] atoms that can be further decomposed into subatomic particles.

An '''overlapping hierarchy'''<!--per WP:R#PLA, this SHOULD be bold--> is a branching hierarchy in which at least one object has two parent objects.<ref name="Dawkins"/> For example, a [[graduate student]] can have two [[research supervisor|co-supervisors]] to whom the student reports directly and equally, and who have the same level of authority within the [[university]] hierarchy (i.e., they have the same [[list of academic ranks|position]] or [[tenure]] status).