Editing Hierarchy (section)

==Nomenclature==
{{see also| Glossary of graph theory| Taxonomy (general)| Structure}}
Hierarchies have their own special vocabulary. These terms are easiest to understand when a hierarchy is diagrammed (see [[#Visually_representing_hierarchies|below]]).

In an organizational context, the following terms are often used related to hierarchies:<ref name="Dawkins"/><ref name="Architecture"/>
* '''[[Non-physical entity|Object]]''': one entity (e.g., a person, department or [[concept]] or element of arrangement or member of a set)
* '''[[System]]''': the entire set of objects that are being arranged hierarchically (e.g., an administration)
* '''[[Dimension]]''': another word for "system" from on-line analytical processing (e.g. cubes)
* '''[[Element (mathematics)|Member]]''': an (element or object) at any (level or rank) in a (class-system, taxonomy or dimension)
*'''Terms about Positioning'''
**'''[[Ranking|Rank]]''': the relative [[value (ethics)|value]], worth, [[complexity]], [[Power (philosophy)|power]], importance, [[authority]], level etc. of an object
**'''[[wikt:level#Noun|Level]] or Tier''': a set of objects with the same rank OR importance
**'''[[Order of precedence|Ordering]]''': the arrangement of the (ranks or levels)
**'''Hierarchy''': the arrangement of a particular set of members into (ranks or levels). Multiple hierarchies are possible per (dimension taxonomy or Classification-system), in which selected levels of the dimension are omitted to flatten the structure
*'''Terms about Placement'''
**'''[[wikt:hierarch|Hierarch]]''', the apex of the hierarchy, consisting of one single orphan (object or member) in the top level of a dimension. The root of an [[Tree structure|inverted-tree structure]]
**'''[[wikt:member|Member]]''', a (member or node) in any level of a hierarchy in a dimension to which (superior and subordinate) members are attached 
**'''[[wikt:orphan|Orphan]]''', a member in any level of a dimension without a parent member. Often the apex of a disconnected branch. Orphans can be grafted back into the hierarchy by creating a relationship (interaction) with a parent in the immediately superior level
**'''[[wikt:leaf|Leaf]]''', a member in any level of a dimension without subordinates in the hierarchy
**'''[[wikt:neighbour|Neighbour]]''': a member adjacent to another member in the same (level or rank). Always a peer.
**'''[[Superior (hierarchy)|Superior]]''': a higher level or an object ranked at a higher level (A parent or an ancestor)
**'''[[wikt:subordinate|Subordinate]]''': a lower level or an object ranked at a lower level (A child or a descendant)
** '''[[Family of sets|Collection]]''': all of the objects at one level (i.e. Peers)
** '''[[wikt:peer|Peer]]''': an object with the same rank (and therefore at the same level)
** '''[[Interpersonal relationship|Interaction]]''': the relationship between an object and its direct superior or subordinate (i.e. a superior/inferior pair)
*** a '''direct''' interaction occurs when one object is on a level exactly one higher or one lower than the other (i.e., on a [[tree (graph theory)|tree]], the two objects have a line between them)
** '''[[Distance (graph theory)|Distance]]''': the minimum number of connections between two objects, i.e., one less than the number of objects that need to be "crossed" to trace a [[path (graph theory)|path]] from one object to another
** '''[[wikt:Span|Span]]''': a [[qualitative data|qualitative]] description of the width of a level when diagrammed, i.e., the number of subordinates an object has
*'''Terms about Nature'''
** '''[[wikt:attribute|Attribute]]''': a heritable characteristic of (members and their subordinates) in a level (e.g. ''hair-colour'')
** '''[[wikt:attribute-value|Attribute-value]]''': the specific value of a heritable characteristic (e.g. ''Auburn'')

In a mathematical context (in [[graph theory]]), the [[Glossary of graph theory|general terminology]] used is different.

Most hierarchies use a more specific vocabulary pertaining to their subject, but the idea behind them is the same. For example, with [[data structure]]s, objects are known as [[node (computer science)|nodes]], superiors are called [[parent node|parents]] and subordinates are called [[child node|children]]. In a business setting, a superior is a [[supervisor|supervisor/boss]] and a peer is a [[Comrade|colleague]].

===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).