Editing Hierarchy

{{short description|System of elements that are subordinated to each other}}
{{Other uses}}
{{Redirect|Subordinate|other uses|Subordination (disambiguation){{!}}Subordination}}
[[File:Die Leiter des Auf- und Abstiegs.jpg|thumb|right|The mediaeval ''scala naturae'' as a staircase, implying the [[orthogenesis|possibility of progress]]:<ref>{{cite book |last=Ruse |first=Michael |author-link=Michael Ruse |date=1996 |title=Monad to man: the Concept of Progress in Evolutionary Biology |url=https://archive.org/details/monadtomanconcep0000ruse |url-access=registration |publisher=Harvard University Press |isbn=978-0-674-03248-4 |pages=[https://archive.org/details/monadtomanconcep0000ruse/page/21 21]–23}}</ref> [[Ramon Llull]]'s ''Ladder of Ascent and Descent of the Mind'', 1305]]
A '''hierarchy''' (from [[Ancient Greek|Greek]]: {{Langx|grc|ἱεραρχία|translit=hierarkhia|lit=rule of a high priest|label=none}}, from {{transliteration|grc|[[ordinary (officer)|hierarkhes]]}}, 'president of sacred rites') is an arrangement of items (objects, names, values, categories, etc.) that are represented as being "above", "below", or "at the same level as" one another. Hierarchy is an important concept in a wide variety of fields, such as [[architecture]], [[philosophy]], [[design]], [[mathematics]], [[computer science]], [[organizational theory]], [[systems theory]], [[systematic biology]], and the [[social sciences]] (especially [[political science]]).

A hierarchy can link entities either directly or indirectly, and either vertically or diagonally. The only direct links in a hierarchy, insofar as they are hierarchical, are to one's immediate superior or to one of one's [[subordinate]]s, although a system that is largely hierarchical can also incorporate alternative hierarchies. Hierarchical links can extend "vertically" upwards or downwards via multiple links in the same direction, following a [[path (graph theory)|path]]. All parts of the hierarchy that are not linked vertically to one another nevertheless can be "horizontally" linked through a path by traveling up the hierarchy to find a common direct or indirect superior, and then down again. This is akin to two [[co-worker]]s or [[Comrade|colleague]]s; each reports to a common superior, but they have the same relative amount of authority. Organizational forms exist that are both alternative and complementary to hierarchy. [[Heterarchy]] is one such form.

==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).

==Etymology==
Possibly the first use of the English word ''hierarchy'' cited by the ''[[Oxford English Dictionary]]'' was in 1881, when it was used in reference to the three orders of three angels as depicted by [[Pseudo-Dionysius the Areopagite]] (5th–6th centuries). Pseudo-Dionysius used the related [[Ancient Greek|Greek]] word (ἱεραρχία, {{transliteration|grc|hierarchia}}) both in reference to the [[De Coelesti Hierarchia|celestial hierarchy]] and the [[Ecclesiastical polity|ecclesiastical hierarchy]].<ref>{{Cite web |url=http://www.newadvent.org/cathen/07322c.htm |title=Catholic Encyclopedia: Hierarchy<!-- Bot generated title --> |access-date=2005-04-27 |archive-date=2021-01-26 |archive-url=https://web.archive.org/web/20210126072002/http://www.newadvent.org/cathen/07322c.htm |url-status=live }}</ref> The Greek term ''hierarchia'' means 'rule of a high priest',<ref>{{cite encyclopedia |url=https://www.etymonline.com/word/hierarchy |title=hierarchy |encyclopedia=[[Online Etymology Dictionary]] |archive-url=https://web.archive.org/web/20180704153523/https://www.etymonline.com/word/hierarchy |archive-date=2018-07-04 |url-status=live}}</ref> from {{transliteration|grc|hierarches}} (ἱεράρχης, 'president of sacred rites, high-priest')<ref>{{cite encyclopedia |url=https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Di%28era%2Frxhs |title=ἱεράρχης |author1=Henry George Liddell |author2=Robert Scott |encyclopedia=[[A Greek–English Lexicon]] |via=Perseus Digital Library |archive-url=https://web.archive.org/web/20210703031946/http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.04.0057:entry=i(era/rxhs |archive-date=2021-07-03 |url-status=live}}</ref> and that from ''hiereus'' (ἱερεύς, 'priest')<ref>{{cite encyclopedia |url=https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Di%28ereu%2Fs |title=ἱερεύς |author1=Henry George Liddell |author2=Robert Scott |encyclopedia=[[A Greek–English Lexicon]] |via=Perseus Digital Library |archive-url=https://web.archive.org/web/20200928172550/http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Di(ereu%2Fs |archive-date=2020-09-28 |url-status=live}}</ref> and ''arche'' (ἀρχή, 'first place or power, rule').<ref>{{cite encyclopedia |url=https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Da%29rxh%2F |title=ἀρχή |author1=Henry George Liddell |author2=Robert Scott |encyclopedia=[[A Greek–English Lexicon]] |via=Perseus Digital Library |archive-url=https://web.archive.org/web/20110606125340/http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.04.0057:entry=a)rxh%2F |archive-date=2011-06-06 |url-status=live}}</ref> Dionysius is credited with first use of it as an abstract noun.

Since hierarchical churches, such as the [[Roman Catholicism|Roman Catholic]] (see [[Catholic Church hierarchy]]) and [[Eastern Orthodoxy|Eastern Orthodox]] churches, had tables of organization that were "hierarchical" in the modern sense of the word (traditionally with [[God in Christianity|God]] as the pinnacle or head of the hierarchy), the term came to refer to similar organizational methods in [[secular]] settings.

=={{anchor|Visually representing hierarchies}}Representing hierarchies==
<!--if you change this section's title, please also change the wikilinks throughout the article that link to it! -->
[[File:Maslow's hierarchy of needs.png|thumb|right|200px|[[Maslow's hierarchy of needs|Maslow's hierarchy of human needs]]. This is an example of a hierarchy visualized with a triangle diagram.  The hierarchical aspect represented here is that needs at lower levels of the pyramid are considered more basic and must be fulfilled before higher ones are met.]]
A hierarchy is typically depicted as a [[pyramid (geometry)|pyramid]], where the height of a level represents that level's status and width of a level represents the quantity of items at that level relative to the whole.<ref>{{cite book | title=Regions of War and Peace | publisher=University of Cambridge | author=Douglas Lemke | year=2002 | location=Cambridge | pages=49}}</ref> For example, the few [[Board of Directors|Directors]] of a company could be at the [[apex (geometry)|apex]], and the [[Base (geometry)|base]] could be thousands of people who have no subordinates.

These pyramids are often [[Diagram|diagrammed]] with a [[triangle]] diagram which serves to emphasize the size differences between the levels (but not all triangle/pyramid diagrams are hierarchical; for example, the 1992 [[History of USDA nutrition guides#Food Guide Pyramid|USDA food guide pyramid]]). An example of a triangle diagram appears to the right.

Another common representation of a hierarchical scheme is as a [[Tree structure|tree diagram]]. [[Phylogenetic trees]], [[charts]] showing the structure of {{section link||Organizations}}, and [[Bracket (tournament)|playoff brackets]] in sports are often illustrated this way.

More recently, as computers have allowed the storage and navigation of ever larger data sets, various methods have been developed to represent hierarchies in a manner that makes more efficient use of the available space on a computer's screen. Examples include [[fractal]] maps, [[treemapping|TreeMaps]] and [[Radial tree|Radial Trees]].

==Visual hierarchy==
In the design field, mainly graphic design, successful layouts and formatting of the content on documents are heavily dependent on the rules of [[visual hierarchy]]. Visual hierarchy is also important for proper organization of files on computers.

An example of visually representing hierarchy is through nested clusters. Nested clusters represent hierarchical relationships using layers of information. The child element is within the parent element, such as in a [[Venn diagram]]. This structure is most effective in representing simple hierarchical relationships. For example, when directing someone to open a file on a computer desktop, one may first direct them towards the main folder, then the subfolders within the main folder. They will keep opening files within the folders until the designated file is located.

For more complicated hierarchies, the stair structure represents hierarchical relationships through the use of visual stacking. Visually imagine the top of a downward staircase beginning at the left and descending on the right. Child elements are towards the bottom of the stairs and parent elements are at the top. This structure represents hierarchical relationships through the use of visual stacking.

==Informal representation==
In plain English, a hierarchy can be thought of as a [[Set (mathematics)|set]] in which:<ref name="Dawkins">{{cite conference|last=Dawkins|first=Richard|author-link=Richard Dawkins|title=Hierarchical organization: a candidate principle for ethology|conference=Growing points in ethology: based on a conference sponsored by St. John's College and King's College, Cambridge|editor1=Bateson, Paul Patrick Gordon |editor2=Hinde, Robert A.|year=1976|publisher=Cambridge University Press|location=Cambridge, England|isbn=0-521-29086-4|pages=7–54}}</ref>
# No element is superior to itself, and
# One element, the (''apex'' or ''hierarch''), is superior to all of the other elements in the set.
The first requirement is also interpreted to mean that a hierarchy can have no [[Cycle (graph theory)|circular relationships]]; the association between two objects is always [[Transitive relation|transitive]].
The second requirement asserts that a hierarchy must have a leader or [[root node|root]] that is common to all of the objects.

==Mathematical representation==
{{Main|Hierarchy (mathematics)}}
Mathematically, in its most general form, a hierarchy is a [[partially ordered set]] or ''poset''.<ref name="Lehmann">{{cite conference|last=Lehmann|first=Fritz|title=Big Posets of Participatings and Thematic Roles|pages=50–74|conference=Conceptual structures: knowledge representation as interlingua—4th International Conference on Conceptual Structures, ICCS '96, Sydney, Australia, August 19–22, 1996—proceedings
|isbn=3-540-61534-2|year=1996|publisher=Springer|editor-last=Eklund|editor-first=Peter G.|editor2-last=Ellis|editor2-first=Gerard|editor3-last=Mann|editor3-first=Graham|series=Lecture Notes in Artificial Intelligence 115|location=Germany}}</ref> The [[#Terminology|system]] in this case is the entire poset, which is constituted of elements. Within this system, each element shares a particular unambiguous property. Objects with the same property value are grouped together, and each of those resulting [[#Terminology|levels]] is referred to as a [[class (set theory)|class]].

"Hierarchy" is particularly used to refer to a poset in which the classes are organized in terms of increasing complexity. <!--Mathematically, a hierarchy can be depicted as a [[combinatorial]] [[object]].-->
Operations such as addition, subtraction, multiplication and division are often performed in a certain sequence or order. Usually, addition and subtraction are performed after multiplication and division has already been applied to a problem. The use of parentheses is also a representation of hierarchy, for they show which operation is to be done prior to the following ones. For example:
(2 + 5) × (7 - 4).
In this problem, typically one would multiply 5 by 7 first, based on the rules of mathematical hierarchy. But when the parentheses are placed, one will know to do the operations within the parentheses first before continuing on with the problem. These rules are largely dominant in algebraic problems, ones that include several steps to solve. The use of hierarchy in mathematics is beneficial to quickly and efficiently solve a problem without having to go through the process of slowly dissecting the problem. Most of these rules are now known as the proper way into solving certain equations.

==Subtypes==
===Nested hierarchy===
<!--if you change this title, change the wiki links within the article that link to it!-->
[[File:Russian-Matroshka no bg.jpg|200px|right|thumb|[[Matryoshka doll]]s, also known as ''nesting dolls'' or ''Russian dolls''. Each doll is encompassed inside another until the smallest one is reached. This is the concept of ''nesting''. When the concept is applied to [[set (mathematics)|sets]], the resulting ordering is a ''nested hierarchy''.]]
A nested hierarchy or ''inclusion hierarchy'' is a hierarchical ordering of [[Nested set collection|nested set]]s.<ref name="natsocsci-ch4">{{cite encyclopedia|title=Hierarchy, Complexity, Society|last=Lane|first=David|pages=81–120|encyclopedia=Hierarchy in Natural and Social Sciences|editor=Pumain, Denise|publisher=[[Springer-Verlag]]|location=New York, New York|year=2006|isbn=978-1-4020-4126-6}}</ref> The concept of nesting is exemplified in Russian [[matryoshka doll]]s. Each doll is encompassed by another doll, all the way to the outer doll. The outer doll holds all of the inner dolls, the next outer doll holds all the remaining inner dolls, and so on. Matryoshkas represent a nested hierarchy where each level contains only one object, i.e., there is only one of each size of doll; a generalized nested hierarchy allows for multiple objects within levels but with each object having only one parent at each level. The general concept is both demonstrated and mathematically formulated in the following example:

: <math> \text{square} \subset \text{quadrilateral} \subset \text{polygon} \subset \text{shape} \, </math>

A square can always also be referred to as a quadrilateral, polygon or shape. In this way, it is a hierarchy. However, consider the set of polygons using this classification. A square can ''only'' be a quadrilateral; it can never be a [[triangle]], [[hexagon]], etc.

Nested hierarchies are the organizational schemes behind [[Taxonomy (general)|taxonomies]] and systematic classifications. For example, using the original [[Linnaean taxonomy]] (the version he laid out in the 10th edition of ''[[Systema Naturae]]''), a human can be formulated as:<ref>{{cite book|title=Systema naturae per regna tria naturae :secundum classes, ordines, genera, species, cum characteribus, differentiis, synonymis, locis|last=Linnaei|first=Carl von|author-link=Carl Linnaeus|year=1959|edition=10th|language=la|url=https://www.biodiversitylibrary.org/bibliography/542|location=[[Stockholm]]|publisher=Impensis Direct|isbn=0-665-53008-0|access-date=2011-09-24|archive-date=2008-10-10|archive-url=https://web.archive.org/web/20081010032456/http://www.biodiversitylibrary.org/bibliography/542|url-status=live}}</ref>

: <math>\text{H. sapiens} \subset \text{Homo} \subset \text{Primates} \subset \text{Mammalia} \subset \text{Animalia}</math>

Taxonomies may change frequently (as seen in [[biological classification|biological taxonomy]]), but the underlying concept of nested hierarchies is always the same.

In many programming taxonomies and syntax models (as well as fractals in mathematics), nested hierarchies, including Russian dolls, are also used to illustrate the properties of [[self-similarity]] and [[recursion]]. Recursion itself is included as a subset of hierarchical programming, and recursive thinking can be synonymous with a form of hierarchical thinking and logic.<ref name=Corballis>{{cite book |first=Michael |last=Corballis |title=The Recursive Mind  |publisher=Princeton University Press |year=2011 |isbn=978-0691145471}}</ref>

===Containment hierarchy===
[[File:Containment Hierarchy example.png|300px|thumb|right|A diagram illustrating a containment hierarchy. The set of all squares is completely contained in the larger set of quadrilaterals, and so on.]]
A containment hierarchy is a direct extrapolation of the [[#Nested hierarchy|nested hierarchy]] concept. All of the ordered sets are still nested, but every set must be "[[strict subset|strict]]"—no two sets can be identical. The shapes example above can be modified to demonstrate this:

: <math> \text{square} \subsetneq \text{quadrilateral} \subsetneq \text{polygon} \subsetneq \text{shape} \, </math>

The notation <math> x \subsetneq y \, </math> means ''x'' is a subset of ''y'' but is not equal to&nbsp;''y''.

A general example of a containment hierarchy is demonstrated in [[inheritance (object-oriented programming)|class inheritance]] in [[object-oriented programming]].

Two types of containment hierarchies are the ''subsumptive'' containment hierarchy and the ''compositional'' containment hierarchy. A subsumptive hierarchy "[[wikt:subsume|subsumes]]" its children, and a compositional hierarchy is "[[wikt:composed|composed]]" of its children. A hierarchy can also be both subsumptive ''and'' compositional{{example needed|date=August 2018}}.<ref name="AI industrial">{{cite encyclopedia|title=Industrial and Engineering Applications of Artificial Intelligence and Expert Systems|last1=Kopisch|first1=Manfred|last2=Günther|first2=Andreas|doi=10.1007/BFb0024994|editor-last=Belli|editor-first=Fevzi|encyclopedia=Industrial and engineering applications of artificial intelligence and expert systems: 5th international conference, IEA/AIE-92, Paderborn, Germany, June 9–12, 1992 : proceedings|year=1992|publisher=[[Springer Science+Business Media|Springer]]|pages=424–427|isbn=3-540-55601-X|series=Lecture Notes in Computer Science Series|volume=602|issn=0302-9743|editor6-last=Radermacher|editor8-first=Franz-Josef|chapter=Configuration of a passenger aircraft cabin based on conceptual hierarchy, constraints and flexible control}}</ref>

===Subsumptive containment hierarchy===
A ''[[Category theory|subsumptive]]'' containment hierarchy is a classification of object classes from the general to the specific. Other names for this type of hierarchy are "taxonomic hierarchy" and "[[is-a|IS-A]] hierarchy".<ref name="Lehmann"/><ref name="ibm">{{cite web|url=http://publib.boulder.ibm.com/infocenter/wtxdoc/v8r2m0/index.jsp?topic=/com.ibm.websphere.dtx.md.doc/concepts/c_map_design_Compositional_Hierarchy.htm|archive-url=https://archive.today/20130103052727/http://publib.boulder.ibm.com/infocenter/wtxdoc/v8r2m0/index.jsp?topic=/com.ibm.websphere.dtx.md.doc/concepts/c_map_design_Compositional_Hierarchy.htm|url-status=dead|archive-date=3 January 2013|title=Compositional hierarchy|work=WebSphere Transformation Extender Design Studio|access-date=9 October 2009}}</ref><ref name="sys model">{{cite book|chapter=An advanced modeling environment based on a hybrid AI-OR approach|chapter-url=https://books.google.com/books?id=ds2eIQ6XZy0C&pg=PA366|pages=366–75|last1=Funke|first1=Birger|last2=Sebastian|first2=Hans-Jürgen|title=Systems modelling and optimization: proceedings of the 18th IFIP TC7 conference|volume=396|series=Research notes in mathematics series|editor1-last=Polis|editor1-first=Michael P.|editor2-last=Dontchev|editor2-first=Asen L.|editor3-last=Kall|editor3-first=Peter|editor4-last=Lascieka|editor4-first=Irena|editor5-last=Olbrot|editor5-first=Andrzej W.|publisher=[[CRC Press]]|year=1999|isbn=978-0-8493-0607-5}}</ref> The last term describes the relationship between each level—a lower-level object "is a" member of the higher class. The taxonomical structure outlined above is a subsumptive containment hierarchy. Using again the example of Linnaean taxonomy, it can be seen that an object that is a member of the level ''Mammalia'' "is a" member of the level ''Animalia''; more specifically, a human "is a" primate, a primate "is a" mammal, and so on. A subsumptive hierarchy can also be defined abstractly as a hierarchy of "[[concept]]s".<ref name="sys model"/> For example, with the Linnaean hierarchy outlined above, an entity name like ''Animalia'' is a way to group all the species that fit the [[wikt:conceptualization|conceptualization]] of an animal.

===Compositional containment hierarchy===
A ''compositional'' containment hierarchy is an ordering of the parts that make up a system—the system is "composed" of these parts.<ref name="Parsons">{{cite book|last=Parsons|first=David|title=Object Oriented Programming in C++|publisher=Cengage Learning|year=2002|pages=110–185|isbn=0-8264-5428-3}}</ref> Most engineered structures, whether natural or artificial, can be broken down in this manner.

The compositional hierarchy that every person encounters at every moment is the [[hierarchy of life]]. Every person can be reduced to [[organ system]]s, which are composed of [[organ (anatomy)|organs]], which are composed of [[tissue (biology)|tissues]], which are composed of [[cells (biology)|cells]], which are composed of [[molecule]]s, which are composed of [[atom]]s. In fact, the last two levels apply to all [[matter]], at least at the [[macroscopic scale]]. Moreover, each of these levels inherit all the properties of their [[#Terminology|children]].

In this particular example, there are also ''[[emergent properties]]''—functions that are not seen at the lower level (e.g., [[cognition]] is not a property of [[neuron]]s but is of the [[Human brain|brain]])—and a scalar quality (molecules are bigger than atoms, cells are bigger than molecules, etc.). Both of these concepts commonly exist in compositional hierarchies, but they are not a required general property. These ''level hierarchies'' are characterized by bi-directional [[Causality|causation]].<ref name="natsocsci-ch4"/> ''Upward causation'' involves lower-level entities causing some property of a higher level entity; children entities may interact to yield parent entities, and parents are composed at least partly by their children. ''[[Downward causation]]'' refers to the effect that the incorporation of entity ''x'' into a higher-level entity can have on ''x'''s properties and interactions. Furthermore, the entities found at each level are ''[[autonomous]]''.

==Contexts and applications==
<!--if you change this section's title, please also change the wikilinks throughout the article that link to it! -->
Kulish (2002) suggests that almost every system of organization which humans apply to the world is arranged hierarchically.<ref name="electrodynamics">{{cite book|title= Hierarchical Methods: Hierarchy and hierarchical asymptotic methods in electrodynamics|last= Kulish|first= V. V.|isbn= 1-4020-0757-4|year= 2002 |volume= 1|publisher= [[Springer Science+Business Media|Springer]]|pages= xvii–xx; 49–71}}</ref>{{request quotation|date=November 2021}} Some conventional definitions of the terms "nation"<ref>{{Cite book|contribution=nation|title=Compact Oxford English Dictionary|contribution-url=http://www.askoxford.com/concise_oed/nation?view=uk|isbn=978-0-19-861022-9|year=1991|title-link=Oxford English Dictionary|last1=Soanes|first1=Catherine|last2=Hawker|first2=Sara|publisher=Oxford University Press |access-date=2009-10-08|archive-date=2007-09-29|archive-url=https://web.archive.org/web/20070929230000/http://www.askoxford.com/concise_oed/nation?view=uk|url-status=dead}}</ref>{{failed verification|date=November 2021}} and "government"<ref>{{Cite book|contribution= government|title= Compact Oxford English Dictionary|contribution-url= http://www.askoxford.com/concise_oed/government?view=uk|isbn= 978-0-19-861022-9|year= 1991|title-link= Oxford English Dictionary|last1= Soanes|first1= Catherine|last2= Hawker|first2= Sara|publisher= Oxford University Press|access-date= 2009-10-08|archive-date= 2007-09-29|archive-url= https://web.archive.org/web/20070929082941/http://www.askoxford.com/concise_oed/government?view=uk|url-status= dead}}</ref>{{failed verification|date=November 2021}} suggest that every [[nation]] has a government and that every government is hierarchical. Sociologists can analyse socioeconomic systems in terms of stratification into a social hierarchy (the [[social stratification]] of societies), and all [[systematic name|systematic classification schemes]] ([[Taxonomy (general)|taxonomies]]) are hierarchical.<ref>{{Cite web |url=https://study.com/academy/lesson/social-stratification-definition-theories-examples.html |access-date=2022-06-24 |website=study.com |title=Social Stratification &#124; Overview, Theories & Examples - Video & Lesson Transcript |archive-date=2022-06-24 |archive-url=https://web.archive.org/web/20220624105232/https://study.com/academy/lesson/social-stratification-definition-theories-examples.html |url-status=live }}</ref> Most [[organized religion]]s, regardless of their internal governance structures, operate as a hierarchy under [[deities]] and [[priesthood]]s. Many [[Christian denomination]]s have an [[autocephalous]] [[Ecclesiastical polity|ecclesiastical hierarchy]] of [[leadership]]. Families can be viewed as hierarchical structures in terms of [[cousinship]] (e.g., first cousin once removed, second cousin, etc.), [[ancestry]] (as depicted in a [[family tree]]) and [[inheritance]] ([[order of succession|succession]] and [[heir]]ship). All the requisites of a well-rounded life and [[lifestyle (sociology)|lifestyle]] can be organized using [[Maslow's hierarchy of needs|Maslow's hierarchy of human needs]] - according to Maslow's hierarchy of human needs. [[Learning]] steps often follow a hierarchical scheme—to master [[differential equation]]s one must first learn [[calculus]]; to learn calculus one must first learn [[elementary algebra]]; and so on. [[Nature]] offers hierarchical structures, as numerous schemes such as [[Linnaean taxonomy]], the [[biological organisation|organization of life]], and [[biomass pyramid]]s attempt to document.<ref>
{{cite book
 |last1                = Dawkins
 |first1               = Richard
 |author-link1         = Richard Dawkins
 |editor-last1         = Bateson
 |editor-first1        = P. P. G.
 |editor-link1         = Patrick Bateson
 |editor-last2         = Hinde
 |editor-first2        = R. A.
 |editor-link2         = Robert Hinde
 |chapter              = Hierarchical organization: a candidate principle for ethology
 |title                = Growing Points in Ethology: based on a conference sponsored by St. John's College and King's College, Cambridge
 |date = 7 October 1976
 |url                  = https://books.google.com/books?id=xIg8AAAAIAAJ
 |location             = Cambridge
 |publisher            = Cambridge University Press
 |publication-date     = 1976
 |page                 = 
 |isbn                 = 9780521212878
 |access-date          = 26 November 2021
 |quote                = 
}} 
</ref>{{request quotation|date=November 2021}}<ref>
{{cite book
 |last1                = Kulish
 |first1               = Viktor Vasylevych
 |author-link1         = 
 |orig-date            = 2002
 |title                = Hierarchical Methods: Hierarchy and Hierarchical Asymptotic Methods in Electrodynamics
 |url                  = https://books.google.com/books?id=0RXnBwAAQBAJ
 |series               = Volume 123 of Fundamental Theories of Physics
 |date = 11 April 2006
 |volume               = 1
 |location             = New York
 |publisher            = Springer Science & Business Media
 |publication-date     = 2006
 |page                 = xviii
 |isbn                 = 9780306480614
 |access-date          = 26 November 2021
 |quote                = At the same time, it is a trivial phenomenon of everyday life, too. Indeed, one can be convinced that there is a hierarchy in everyday life everywhere. We can affirm once more that a person lives in a completely hierarchical world.
}} 
</ref>

While the above examples are often{{quantify|date=November 2021}} clearly depicted in a hierarchical form and are classic examples, hierarchies exist in numerous systems where this branching structure is not immediately apparent. For example, most [[postal code|postal-code]] systems are hierarchical. Using the [[Postal codes in Canada|Canadian postal code system]] as an example, the top level's binding concept, the [[forward sortation area|"postal district"]], consists of 18 objects (letters). The next level down is the "zone", where the objects are the digits 0–9. This is an example of an [[#Degree_of_branching|overlapping hierarchy]], because each of these 10 objects has 18 parents. The hierarchy continues downward to generate, in theory, 7,200,000 unique codes of the format ''A0A 0A0'' (the second and third letter positions allow 20 objects each). Most [[library classification]] systems are also hierarchical. The [[Dewey Decimal Classification|Dewey Decimal System]] is infinitely hierarchical because there is no finite bound on the number of digits can be used after the decimal point.<ref name="Dewey">{{cite web|title=Tracking Nuclear Sources|date=May–June 2009|last= Walker |first= Randy|publisher=wellservicingmagazine.com|pages=28–30|url= http://wellservicingmagazine.com/sites/default/files/pdfmag/WSM_MAYJUN09.PDF}}{{dead link|date= November 2017 |bot=InternetArchiveBot |fix-attempted=yes}}</ref>

[[File:Organizational chart.svg|thumb|200px|A simple military [[hierarchical organization|organizational hierarchy]] depicted in the form of a [[tree structure|tree]]. Diagrams like this exemplify [[organizational chart]]s.]]

===Organizations===
{{Main|Organizational structure| Hierarchical organization}}

[[Organization]]s can be structured as a [[dominance hierarchy]]. In an organizational hierarchy, there is a single person or group with the most [[power (philosophy)|power]] or [[authority]], and each subsequent level represents a lesser authority. Most organizations are structured in this manner,<ref>{{Cite web |url=https://study.com/academy/lesson/organizational-chart-and-hierarchy-definition-examples.html |access-date=2022-06-24 |website=study.com |title=Organizational Chart and Hierarchy: Definition & Examples - Video & Lesson Transcript |archive-date=2022-06-24 |archive-url=https://web.archive.org/web/20220624105529/https://study.com/academy/lesson/organizational-chart-and-hierarchy-definition-examples.html |url-status=live }}</ref> including [[Forms of government|governments]], [[Company|companies]], [[Military|armed forces]], [[militia]] and [[organized religion]]s. The units or persons within an organization may be depicted hierarchically in an [[organizational chart]].

In a [[reverse hierarchy]], the conceptual [[pyramid (geometry)|pyramid]] of authority is turned upside-down, so that the apex is at the bottom and the base is at the top. This mode represents the idea that members of the higher rankings are responsible for the members of the lower rankings.

=== Biology ===
{{Main|Biological organisation#Fundamentals}}

Empirically, when we observe in nature a large proportion of the (complex) biological systems, they exhibit hierarchic structure.<ref>{{Cite journal |last=Simon |first=Herbert A. |date=1962 |title=The Architecture of Complexity |url=https://www.jstor.org/stable/985254 |journal=Proceedings of the American Philosophical Society |volume=106 |issue=6 |pages=467–482 |jstor=985254 |issn=0003-049X |access-date=2022-06-24 |archive-date=2022-06-24 |archive-url=https://web.archive.org/web/20220624110921/https://www.jstor.org/stable/985254 |url-status=live }}</ref> On theoretical grounds we could expect complex systems to be hierarchies in a world in which complexity had to evolve from simplicity.<ref>{{Cite web |title=Artificial Intelligence - foundations of computational agents -- 2 Agent Architectures and Hierarchical Control |url=https://artint.info/html/ArtInt_33.html |access-date=2022-06-24 |website=artint.info |archive-date=2022-07-04 |archive-url=https://web.archive.org/web/20220704035951/http://artint.info/html/ArtInt_33.html |url-status=live }}</ref> [[Systems theory|System]] hierarchies analysis performed in the 1950s,<ref>{{harvnb|Evans|1951}}</ref><ref>{{harvnb|Evans|1956}}</ref> laid the empirical foundations for a [[Branches of science|field]] that would become, from the 1980s, '''hierarchical ecology'''.<ref>{{harvnb|Margalef|1975}}</ref><ref>{{harvnb|O'Neill|1986}}</ref><ref>{{harvnb|Wicken|Ulanowicz|1988}}</ref><ref>{{harvnb|Pumain|2006}}</ref><ref>{{harvnb|Jordan|Jørgensen|2012}}</ref>

The theoretical foundations are summarized by [[thermodynamics]].
When [[biological systems]] are modeled as [[physical system]]s, in the most general abstraction, they are [[Thermodynamic system#Open system|thermodynamic open systems]] that exhibit [[self-organisation|self-organised]] behavior, and the [[Set theory|set/subset]] relations between [[dissipative structures]] can be characterized{{by whom|date=November 2021}} in a hierarchy.

Other hierarchical representations related to biology include [[ecological pyramids]] which illustrate energy flow or [[trophic levels]] in [[ecosystems]], and [[Taxonomy (general)|taxonomic]] hierarchies, including the [[Linnean classification]] scheme and [[phylogenetic trees]] that reflect inferred patterns of evolutionary relationship among living and extinct species.

===Computer-graphic imaging===
{{Main|3D modeling}}
[[Computer-generated imagery|CGI]] and [[computer animation|computer-animation]] [[computer program|programs]] mostly use hierarchies for models. On a [[3D computer graphics|3D]] model of a [[human]] for example, the [[chest]] is a [[parent]] of the upper left arm, which is a parent of the lower left arm, which is a parent of the [[hand]]. This pattern is used in [[3D modeling|modeling]] and [[animation]] for almost everything built as a 3D [[Digital data|digital]] model.

===Linguistics===
Many grammatical theories, such as [[phrase-structure grammar]], involve hierarchy.

[[Direct–inverse language]]s such as [[Cree language|Cree]] and [[Mapudungun language|Mapudungun]] distinguish subject and object on [[verb]]s not by different subject and object markers, but via a hierarchy of persons.

In this system, the three (or four with [[Algonquian languages]]) persons occur in a hierarchy of [[salience (language)|salience]]. To distinguish which is subject and which object, ''inverse markers'' are used if the object outranks the subject.

On the other hand, languages include a variety of phenomena that are not hierarchical. For example, the relationship between a pronoun and a prior noun-phrase to which it refers commonly crosses grammatical boundaries in non-hierarchical ways.

===Music===
The structure of a musical composition is often understood hierarchically (for example by [[Heinrich Schenker]] (1768–1835, see [[Schenkerian analysis]]), and in the (1985) [[Generative theory of tonal music|Generative Theory of Tonal Music]], by composer [[Fred Lerdahl]] and linguist Ray [[Jackendoff]]). The sum of all notes in a piece is understood to be an all-inclusive surface, which can be reduced to successively more sparse and more fundamental types of motion. The levels of structure that operate in Schenker's theory are the foreground, which is seen in all the details of the musical score; the middle ground, which is roughly a summary of an essential contrapuntal progression and voice-leading; and the background or [[Ursatz]], which is one of only a few basic "long-range counterpoint" structures that are shared in the gamut of tonal music literature.

The [[pitch (music)|pitches]] and [[Musical form|form]] of [[Tonality|tonal]] music are organized hierarchically, all pitches deriving their importance from their relationship to a [[Tonic (music)|tonic]] key, and secondary themes in other  [[Key signature|keys]] are brought back to the tonic in a recapitulation of the primary theme.

=== Examples of other applications ===
<!-- This section is for direct examples of a hierarchical system ONLY, and only ones that have not been summarized above. Methodologies belong in the appropriate section below. Related concepts are listed under the "See also" section. If you are uncertain where a link belongs, place it in the "See also" section. HINT: If you can't easily say what it's a hierarchy OF, it doesn't belong here (but that doesn't imply that if you can say what its a hierarchy of, it belongs here). -->

{{col-begin}}
{{col-3}}
==== Information-based ====
<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "information-based hierarchies"-->
* [[Library classification]]
** [[Dewey Decimal Classification]]
{{col-3}}
==== City planning-based ====
<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "city planning-based hierarchies"-->
* [[Green transport hierarchy]]
* [[Hierarchy of roads|Roads]]
** [[Street hierarchy|Streets]]
* [[Settlement hierarchy]]
** [[Settlement hierarchy#Example of a settlement hierarchy|As of 2010]]
** [[Ekistic units|As of 2100 (estimate according to Doxiadis, 1968)]]
{{col-3}}

==== Linguistics-oriented ====
<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "linguistics-oriented hierarchies"-->
* [[Tree model|Language family tree]]
* [[Levels of adequacy|Levels of adequacy for evaluating grammars]]
* [[Direct–inverse language]]s
* [[Structural linguistics]]
** [[Parse tree]]
** [[Formal grammar]]s
** [[Abstract syntax tree]]
* [[Color terms#Basic color terms|Evolution of basic color terminology in languages]]
{{col-end}}

{{col-begin}}
{{col-3}}

==== Power- or authority-based ====
<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "power- or authority-based hierarchies"-->
* [[Noble ranks|Aristocratic hierarchies]]
** In [[Royal and noble ranks#General chart of "translations" between languages|Europe]]
** In [[Chinese nobility#Sovereign and ruling family ranks|China]]
* [[Ecclesiastical polity|Ecclesiastical hierarchies]]
** [[Catholic Church hierarchy]]
** [[Priesthood (LDS Church)|LDS Church hierarchy]]
** [[Kimbanguism#Hierarchy|Kimbanguist Church hierarchy]]
** [[Raëlism#Member hierarchy|Raëlism Church hierarchy]]
** see also [[autocephaly]]
* [[Prussian three-class franchise]]<ref>
{{cite book
 |last1                = Tipton
 |first1               = Frank
 |author-link1         = Frank Tipton
 |chapter              = Politics, Governance, and Diplomacy between Neoclassicism and Modernism
 |title                = A History of Modern Germany Since 1815
 |date = January 2003
 |url                  = https://books.google.com/books?id=SQGMYLJRdXoC
 |location             = London
 |publisher            = A&C Black
 |publication-date     = 2003
 |page                 = 239
 |isbn                 = 9780826449108
 |access-date          = 26 November 2021
 |quote                = Kühne believes the Prussian franchise lasted for over sixty years because it accurately reflected the social realities of the relatively closed, hierarchical, and conformist communities of rural Prussia.
}} 
</ref>
* Political party hierarchies
** [[Ranks and insignia of the Nazi Party|Nazi Party]] (''pace'' overlapping fields<ref>
Compare:
{{cite book
 |last1                = Lee
 |first1               = Stephen J.
 |orig-date            = 1987
 |chapter              = Dictatorship in Germany
 |title                = European Dictatorships 1918-1945
 |date = 12 February 2016
 |url                  = https://books.google.com/books?id=D32PCwAAQBAJ
 |edition              = 4, revised
 |location             = London
 |publisher            = Routledge
 |publication-date     = 2016
 |page                 = 217
 |isbn                 = 9781317294221
 |access-date          = 26 November 2021
 |quote                = [...] Nazi administration is now regarded as an overlapping and confusing 'polycracy'. The basis of the criticism is that the multi-layering of agencies and the lack of proper delineation between them generated conflict and hampered efficiency. There was, for example, extensive rivalry between the Four-Year plan Office, the Ministry of Economics, the War ministry and the Plenipotentiary for Economics.
}} 
</ref>)
*** [[SS Ranks#Final SS ranks 1934–1945|SS]]
*** [[Glossary of Nazi Germany#G|Hierarchy of subdivisions within the Gau]]
** [[Communist Party of the Soviet Union#Structure|Communist Party of the Soviet Union]]
** [[Chinese Communist Party]]
* [[Command hierarchy|Chain of command]]
** [[List of comparative military ranks|Military ranks]]
** [[Military organization#Hierarchy of modern armies|Military units]]
** [[Unified Combatant Command|U.S. Military Combatant Commands]]
* [[Dominance hierarchy|Intraspecial dominance]]
** [[Pecking order]]
* [[Social stratification|Social classes]]
** [[Caste system in India]]
** [[Hierarchical structure of Feudal Japan]]
** [[Master race#Hierarchy|White racist hierarchy]]
** [[Hierarchy of Exclusion]] (Ender's Game)

{{col-3}}

==== Value-related ====
<!--value meaning both money and relative importance--> <!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "value-related hierarchies"-->
* [[Hierarchy of genres|Hierarchy of genres in art]]
* [[Hierarchy of evidence|Evidence]]
* [[Maslow's hierarchy of needs|Human needs]]
* [[Hierarchy of precious substances|Precious substances]]
* [[Hierarchy of values|Judicial hierarchy of social values]]

{{col-3}}

==== Perception-based ====
<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "perception-based hierarchies"-->
* [[Color wheel]]
** [[Primary colors]]
*** [[Secondary colors]]
**** [[Tertiary colors]]
{{col-end}}

{{col-begin}}
{{col-3}}

==== History-oriented ====
<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "history-oriented hierarchies"-->
* [[Three-age system]]
* [[Comparative history|Cyclic theory of civilization]]
** [[Spengler's civilization model|Oswald Spengler]]
** [[A Study of History#List of civilizations|Arnold J. Toynbee]]
* [[Spiral dynamics]]

{{col-3}}

==== Science-focussed ====
 <!--[[WP:HYPHEN]]—this category's logical title is "science-focussed hierarchies"-->
* [[Earth's location in the universe#Earth in the universe|Hierarchy of organization within the Universe]]
* [[Hierarchical ternary star system|Star systems]]
* [[Biological classification]]
* [[Biological organization]]
* [[Phylogenetic tree]]
* [[Timeline of evolution|Evolutionary development]]
* [[Ecological land classification#Hierarchy of classification levels in ecology compared to other fields|Hierarchy of ecological georegions]]

{{col-3}}

==== Technology-based ====
* [[Memory hierarchy]]
** [[Cache hierarchy]]
* [[Hierarchical clustering|Clusters]]
* [[Hierarchy (object-oriented programming)|Class constructs]]
* [[Hierarchical database model|Data organization]]
** [[Hierarchical query]]
* [[Hierarchical Data Format|Data storage]]
** [[Hierarchical file system|Computer files]]
* [[Hierarchical control system|Devices]]
* [[Classless Inter-Domain Routing|IP addresses]]
* [[Memory hierarchy|Memory]]
** [[Hierarchical page tables|Virtual memory allocation]]
* [[Hierarchical internetworking model|Networks]]
* [[Hierarchical cell structure|Radio cells]]
* [[Hierarchical state machine|States (configurations)]]
* [[Hierarchical name space|Web addresses]]
* [[Structure]]
** [[Data Structure]]
* [[Inheritance (object-oriented programming)]]
{{col-end}}

==== Religion-related ====
<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "religion- and mythology-related hierarchies"-->
* Levels of consciousness
**[[Chakra#The seven major chakras|Chakras]]
**[[Great chain of being]]
**[[Ray of Creation|G.I. Gurdjieff]]
**[[Eight Circuit Model of Consciousness#The eight circuits|Timothy Leary]]
* Levels of spiritual development
** In [[Four stages of enlightenment|Theravada Buddhism]]
** In [[Bhumi (Buddhism)|Mahayana Buddhism]]
* Ages in the evolution of society
** In [[Astrological age#Past ages|Astrology]]
** In [[Ages of Man|Hellenism (the Ancient Greek Religion)]]
**[[Dispensation (period)#Protestant dispensations|Dispensations in Protestantism]]
**[[Dispensation (period)#Latter Day Saint dispensations|Dispensations in Mormonism]]
*[[Hierarchical communion|Degrees of communion between various Christian churches]]
*[[UFO religion]]s
**[[Master Jesus#Airborne Division of the Brotherhood of Light|Command hierarchy of the ''Ashtar Galactic Command'' flying saucer fleet]]
* Deities
** In [[Japanese Buddhist pantheon#Hierarchical structure of the Buddhist pantheon|Japanese Buddhism]]
** In [[Spiritual Hierarchy#Levels of the spiritual hierarchy|Theosophy]]
* Angels
** In [[Christian angelic hierarchy|Christianity]]
** In [[Islamic view of angels#Angel hierarchy|Islam]]
** In [[Jewish angelic hierarchy|Judaism]]
***[[Kabbalistic angelic hierarchy|Kabbalistic]]
** In [[Yazata|Zoroastrianism]]
* Devils and Demons
**[[Hierarchy of devils|Devils]]
**[[Hierarchy of demons|Demons]]
*[[Hell]]s
** In [[Inferno (Dante)|Catholicism (Nine Levels of Hell)]]
** In [[Naraka (Buddhism)|Buddhism (Sixteen Levels of Hell)]]
*[[Religious stratification|Religions in society]]
* (organizational&nbsp;hierarchies are listed under {{nowrap|"[[#Power- or authority-based|Power- or authority-based]]"}})<!--non-breaking spaces used for neatness at all resolutions-->

===Methods using hierarchy===
<!-- See note at "Examples of other applications"-->
{{columns-list|colwidth=22em|
* [[Analytic Hierarchy Process]]
** [[Hierarchical Decision Process]]
* [[HOOD method|Hierarchic Object-Oriented Design]]
* [[Hierarchical Bayes model]]
* [[Hierarchical clustering]]
** [[Hierarchical clustering of networks]]
* [[Hierarchical constraint satisfaction]]
* [[Hierarchical linear modeling]]
* [[Hierarchical modulation]]
* [[Hierarchical proportion]]
* [[Hierarchical RBF|Hierarchical radial basis function]]
* [[Hierarchical storage management]]
* [[Hierarchical task network]]
* [[Hierarchical temporal memory]]
* [[Hierarchical Token Bucket|Hierarchical token bucket]]
* [[Hierarchical visitor pattern]]
* [[Presentation-abstraction-control]]
** [[Hierarchical-Model-View-Controller]]
}}

== Criticisms ==
{{Unreferenced section|date=September 2024}}
In the work of diverse theorists such as [[William James]] (1842 to 1910), [[Michel Foucault]] (1926 to 1984) and [[Hayden White]] (1928 to 2018), important critiques of hierarchical [[epistemology]] are advanced. James famously asserts in his work [[Radical Empiricism]] that clear distinctions of type and category are a constant but unwritten goal of scientific reasoning, so that when they are discovered, success is declared. But if aspects of the world are organized differently, involving inherent and intractable ambiguities, then scientific questions are often considered unresolved.

[[Feminists]], [[Marxists]], [[anarchists]], [[communists]], [[critical theorists]] and others, all of whom have multiple interpretations, criticize the hierarchies commonly found within human society, especially in social relationships. Hierarchies are present in all parts of society: in businesses, schools, families, etc. These relationships are often viewed as necessary. Entities that stand in hierarchical arrangements are animals, humans, plants, etc.

===Ethics, behavioral psychology, philosophies of identity===
[[File:Hierarchy Of Purposes.jpg|thumb|right|alt=|Career-oriented purposes can be diagrammed using a hierarchy describing how less important actions support a larger goal.]]
In [[ethics]], various [[virtues]] are enumerated and sometimes organized hierarchically according to certain brands of [[virtue theory]].

In some of these random examples, there is an asymmetry of 'compositional' significance between levels of structure, so that small parts of the whole hierarchical array depend, for their meaning, on their membership in larger parts. There is a hierarchy of activities in human life: productive activity serves or is guided by the moral life; the moral life is guided by practical reason; practical reason (used in moral and political life) serves contemplative reason (whereby we contemplate God). Practical reason sets aside time and resources for contemplative reason.

==See also==
<!-- See note at "Further applications"-->
{{columns-list|colwidth=26em|
* {{annotated link|Anarchy}}
* {{annotated link|Class browser}}
* {{annotated link|Forms of government}}
* {{annotated link|Graph theory}}
* {{annotated link|Heterarchy}}
* {{annotated link|Hierarchical classifier}}
* {{annotated link|Hierarchical epistemology}}
* {{annotated link|Hierarchical hidden Markov model}}
* {{annotated link|Hierarchical INTegration}}
* {{annotated link|Hierarchical organization}}
* {{annotated link|Hierarchical Music Specification Language}}
* {{annotated link|Hierarchy Open Service Interface Definition}}
* {{annotated link|Hierarchy problem}}
* {{section link|Holarchy|Different meanings}}
* {{annotated link|Instrumental value}}
* {{annotated link|Layer (disambiguation)}}
* {{annotated link|Multilevel model}}
* {{annotated link|Multitree}} 
* {{annotated link|Ordinary (officer)}}
** {{section link|Characters of Halo|High Prophets}}
** {{annotated link|List of Coptic Orthodox Popes of Alexandria}}
* {{annotated link|Peter Principle}}
* {{annotated link|Ring (computer security)}}
* {{annotated link|Social dominance theory}}

}}

===Structure-related concepts===
''(For example, in {{section link||Subtypes}})''
* [[Is-a]]
** [[Hypernymy]] (and [[supertype]])
** [[Hyponymy]] (and [[Subtyping|subtype]])
* [[Has-a]]
** [[Holonymy]]
** [[Meronymy]]

==Footnotes==
{{Reflist}}

===Works cited===
{{refbegin|2}}
* {{Citation |last=Evans |year=1951 |first=F. C. |title=Ecology and urban areal research |journal=Scientific Monthly |issue=73}}
* {{Citation |last=Evans |year=1956 |first=F. C. |title=Ecosystem as basic unit in ecology |pmid=17793430 |doi=10.1126/science.123.3208.1127 |volume=123 |journal=Science |issue=3208 |pages=1127–8 |bibcode=1956Sci...123.1127E}}
* {{Citation |last1=Jordan |last2=Jørgensen |year=2012 |first1=F. |first2=S. E. |title=Models of the Ecological Hierarchy: From Molecules to the Ecosphere |publisher=Newnes |isbn=9780444593962}}
* {{Citation |last=Margalef |year=1975 |first=R. |title=External factors and ecosystem stability |doi=10.1007/BF02505181 |volume=37 |journal=Schweizerische Zeitschrift für Hydrologie |issue=1 |pages=102–117 |bibcode=1975AqSci..37..102M |s2cid=20521602|hdl=10261/337692 |hdl-access=free }}
* {{Citation |last=O'Neill |year=1986 |first=R. V. |title=A Hierarchical Concept of Ecosystems |publisher=Princeton University Press |isbn=0691084378 |url-access=registration |url=https://archive.org/details/hierarchicalconc00onei}}
* {{Citation |last1=Wicken |last2=Ulanowicz |year=1988 |first1=J. S. |first2=R. E. |title=On quantifying hierarchical connections in ecology |doi=10.1016/0140-1750(88)90066-8 |volume=11 |journal=Journal of Social and Biological Systems |issue=3 |pages=369–377}}
{{refend}}

==Further reading==
* {{cite book|first1=Valerie|last1=Ahl|first2=Timothy F. H.|last2=Allen|author-link2=Timothy F. H. Allen|year=1996|title=Hierarchy Theory|location=New York|publisher=Columbia University Press|isbn=0-231-08481-1}}
* {{cite conference|last1=Akl |first1=Selim G. |author-link=Selim Akl |last2=Taylor |first2=Peter D. |title=Cryptographic solution to a multilevel security problem |conference=Advances in Cryptology – Proceedings of [[CRYPTO]] '82 |pages=237–249 |publisher=[[Plenum Publishing Corporation]] |year=1983 |location=New York |url=http://dsns.csie.nctu.edu.tw/research/crypto/HTML/PDF/C82/237.PDF |archive-url=https://web.archive.org/web/20021229212150/http://dsns.csie.nctu.edu.tw/research/crypto/HTML/PDF/C82/237.PDF |url-status=dead |archive-date=2002-12-29 |isbn=0-306-41366-3}}
* {{cite journal | last1 = Carbone | first1 = June | last2 = Cahn | first2 = Naomi |title= Is marriage for rich men? |journal = [[Nevada Law Journal]]| volume = 13 | issue = 2 | page = 6 | publisher = [[William S. Boyd School of Law]] | url = http://scholars.law.unlv.edu/nlj/vol13/iss2/6 | date = 2013}}
* {{cite thesis|title=Regulatory hierarchies in auxin signal transduction and vascular tissue development|last=Ckurshumova|first=Wenzislava|isbn=978-0-494-27682-2|year=2007|degree=PhD|url=https://hdl.handle.net/1807/118234|at=Section B|publisher=University of Toronto|hdl=1807/118234 }}
* {{Cite book|last1=Galindo|first1=Cipriano|last2=Fernández-Madrigal|first2=Juan-Antonio|title=Multiple Abstraction Hierarchies for Mobile Robot Operation in Large Environments|series=Studies in Computational Intelligence|editor-last=Kacprzyk|editor-first=Janusz|year=2007|publisher=Springer Berlin Heidelberg|location=Berlin|isbn=978-3-540-72688-3}}
* {{cite journal|first=Julie|last=Nelson|author-link=Julie Nelson (economist)|year=1992|title=Gender, Metaphor and the Definition of Economics|journal=Economics and Philosophy|volume=8|issue=1|pages=103–25|doi=10.1017/S026626710000050X|s2cid=146493891 }}
* {{cite book|last=Pumain|first=Denise|title=Hierarchy in Natural and Social Sciences|publisher=[[Springer-Verlag]]|location=New York, New York|year=2006|isbn=978-1-4020-4126-6}}
* {{cite book|first=A.|last=Rosenbaum|author-link=Alexis Rosenbaum|year=2000|title=Les représentations hiérarchiques en philosophie|language=fr|location=Paris|publisher=Desclee de Brouwer}}
* {{cite thesis|title=Improving classification models when a class hierarchy is available|last=Shahbaba|first=Babak|isbn=978-0-494-28076-8|at=Section B|publisher=University of Toronto|year=2007|hdl=1807/119833 |degree=PhD|url=https://hdl.handle.net/1807/119833}}
** Also includes full copies of:
** {{cite journal|title=Improving Classification When a Class Hierarchy is Available Using a Hierarchy-Based Prior|last1=Shahbaba|first1=Babak|last2=Neal|first2=Radford M.|journal=Bayesian Analysis|volume=2|issue=1|pages=221–228|year=2007|issn=1936-0975|publisher=[[International Society for Bayesian Analysis]]|location=[[Carnegie Mellon University]], Pittsburgh, Pennsylvania|url=http://ba.stat.cmu.edu/journal/2007/vol02/issue01/shahbaba.pdf|bibcode=2005math.....10449S|arxiv=math/0510449|doi=10.1214/07-ba209|s2cid=10611032|url-status=dead|archive-url=https://web.archive.org/web/20150903231224/http://ba.stat.cmu.edu/journal/2007/vol02/issue01/shahbaba.pdf|archive-date=2015-09-03}}
** {{cite journal|last1=Shahbaba|first1=Babak|last2=Neal|first2=Radford M.|title=Gene function classification using Bayesian models with hierarchy-based priors|journal=[[BMC Bioinformatics]]|publisher=[[BioMed Central]]|location=London, England|year=2006|volume=7|page=448|doi=10.1186/1471-2105-7-448|pmc=1618412|pmid=17038174|issn=1471-2105|bibcode=2006q.bio.....5015S|arxiv=q-bio/0605015 |doi-access=free }}

==External links==
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{{Political philosophy}}
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[[Category:Hierarchy| ]]
[[Category:Patterns]]
[[Category:Structure]]
[[Category:Political culture]]