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<title>Tree structure</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Tree structure</span></span>

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<p>A <b>tree structure</b>, <b>tree diagram</b>, or <b>tree model</b> is a way of representing the <a href="Hierarchy" title="Hierarchy">hierarchical</a> nature of a <a href="Structure" title="Structure">structure</a> in a graphical form. It is named a "tree structure" because the classic <a href="#Representing_trees">representation</a> resembles a <a href="Tree" title="Tree">tree</a>, although the chart is generally upside down compared to a biological tree, with the "stem" at the top and the "leaves" at the bottom.

</p><p>A tree structure is conceptual, and appears in several forms. For a discussion of tree structures in specific fields, see <a href="Tree_(data_structure)" class="mw-redirect" title="Tree (data structure)">Tree (data structure)</a> for computer science; insofar as it relates to graph theory, see <a href="Tree_(graph_theory)" title="Tree (graph theory)">tree (graph theory)</a> or <a href="Tree_(set_theory)" title="Tree (set theory)">tree (set theory)</a>. Other related articles are listed below.

</p>

<div class="mw-heading mw-heading2"><h2 id="Terminology_and_properties">Terminology and properties</h2></div>

<p>The tree elements are called "<a href="Node_(computer_science)" title="Node (computer science)">nodes</a>".

The lines connecting elements are called "branches".

Nodes without children are called <a href="Leaf_node" class="mw-redirect" title="Leaf node">leaf nodes</a>, "end-nodes", or "leaves".

</p><p>Every <a href="Finite_set" title="Finite set">finite</a> tree structure has a member that has no <a href="Superior_(hierarchy)" title="Superior (hierarchy)">superior</a>. This member is called the "root" or <a href="Root_node" class="mw-redirect" title="Root node">root node</a>. The root is the starting node. But the converse is not true: infinite tree structures may or may not have a root node.

</p><p>The names of relationships between nodes model the <a href="Kinship_terminology" title="Kinship terminology">kinship terminology</a> of family relations. The gender-neutral names "parent" and "child" have largely displaced the older "father" and "son" terminology. The term "uncle" is still widely used for other nodes at the same level as the parent, although it is sometimes replaced with gender-neutral terms like "ommer".<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p>

<ul><li>A node's "parent" is a node one step higher in the hierarchy (i.e. closer to the root node) and lying on the same branch.</li>

<li>"Sibling" ("brother" or "sister") nodes share the same parent node.</li>

<li>A node's "uncles" (sometimes "ommers") are siblings of that node's parent.</li>

<li>A node that is connected to all lower-level nodes is called an "ancestor". The connected lower-level nodes are "descendants" of the ancestor node.</li></ul>

<p>In the example, "encyclopedia" is the parent of "science" and "culture", its children. "Art" and "craft" are siblings, and children of "culture", which is their parent and thus one of their ancestors. Also, "encyclopedia", as the root of the tree, is the ancestor of "science", "culture", "art" and "craft". Finally, "science", "art" and "craft", as leaves, are ancestors of no other node.

</p><p>Tree structures can depict all kinds of <a href="Taxonomy_(general)" class="mw-redirect" title="Taxonomy (general)">taxonomic</a> knowledge, such as <a href="Family_tree" title="Family tree">family trees</a>, the biological <a href="Evolutionary_tree" class="mw-redirect" title="Evolutionary tree">evolutionary tree</a>, the <a href="Indo-European_languages#Classification" title="Indo-European languages">evolutionary tree of a language family</a>, the <a href="Generative_grammar#Context-free_grammars" title="Generative grammar">grammatical structure</a> of a language (a key example being S → NP VP, meaning a sentence is a noun phrase and a verb phrase, with each in turn having other components which have other components), the way web pages are logically ordered in a web site, <a href="Tree_of_primitive_Pythagorean_triples" title="Tree of primitive Pythagorean triples">mathematical trees of integer sets</a>, et cetera.

</p><p>The <a href="Oxford_English_Dictionary" title="Oxford English Dictionary">Oxford English Dictionary</a> records use of both the terms "tree structure" and "tree-diagram" from 1965 in <a href="Noam_Chomsky" title="Noam Chomsky">Noam Chomsky</a>'s <i><a href="Aspects_of_the_Theory_of_Syntax" title="Aspects of the Theory of Syntax">Aspects of the Theory of Syntax</a></i>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

</p><p>In a tree structure there is one and only one <a href="Path_(graph_theory)" title="Path (graph theory)">path</a> from any point to any other point.

</p><p><a href="Computer_science" title="Computer science">Computer science</a> uses tree structures extensively (<i>see</i> <a href="Tree_(data_structure)" class="mw-redirect" title="Tree (data structure)">Tree (data structure)</a> and <a href="Telecommunications" title="Telecommunications">telecommunications</a>.)

</p><p>For a formal definition see <a href="Tree_(set_theory)" title="Tree (set theory)">set theory</a>, and for a generalization in which children are not necessarily successors, see <a href="Prefix_order" title="Prefix order">prefix order</a>.

</p>

<div class="mw-heading mw-heading2"><h2 id="Examples_of_tree_structures">Examples of tree structures</h2></div>

<ul><li>Internet:

<ul><li><a href="Usenet_hierarchy" class="mw-redirect" title="Usenet hierarchy">usenet hierarchy</a></li>

<li><a href="Document_Object_Model" title="Document Object Model">Document Object Model</a>'s logical structure,<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> <a href="Yahoo!" class="mw-redirect" title="Yahoo!">Yahoo!</a> subject index, <a href="Curlie" class="mw-redirect" title="Curlie">Curlie</a></li></ul></li>

<li><a href="Operating_system" title="Operating system">Operating system</a>: <a href="Directory_structure" title="Directory structure">directory structure</a></li>

<li>Information management: <a href="Dewey_Decimal_Classification" title="Dewey Decimal Classification">Dewey Decimal System</a>, <a href="Polythematic_Structured_Subject_Heading_System" title="Polythematic Structured Subject Heading System">PSH</a>, this hierarchical bulleted list</li>

<li>Management: hierarchical <a href="Organization" title="Organization">organizational</a> structures</li>

<li>Computer science:

<ul><li><a href="Binary_search_tree" title="Binary search tree">binary search tree</a></li>

<li><a href="Red%E2%80%93black_tree" title="Red–black tree">red–black tree</a></li>

<li><a href="Doubly_logarithmic_tree" title="Doubly logarithmic tree">doubly logarithmic tree</a></li></ul></li>

<li>Biology: <a href="Evolutionary_tree" class="mw-redirect" title="Evolutionary tree">evolutionary tree</a></li>

<li>Business: <a href="Pyramid_selling_scheme" class="mw-redirect" title="Pyramid selling scheme">pyramid selling scheme</a></li>

<li>Project management: <a href="Work_breakdown_structure" title="Work breakdown structure">work breakdown structure</a></li>

<li>Linguistics:

<ul><li>(Syntax) <a href="Phrase_structure_rules" title="Phrase structure rules">Phrase structure trees</a></li>

<li>(Historical Linguistics) <a href="Tree_model" title="Tree model">Tree model</a> of language change</li></ul></li>

<li>Sports: <a href="Business_chess" title="Business chess">business chess</a>, <a href="Bracket_(tournament)" title="Bracket (tournament)">playoffs brackets</a></li>

<li>Mathematics: <a href="Von_Neumann_universe" title="Von Neumann universe">Von Neumann universe</a></li>

<li>Group theory: <a href="Descendant_tree_(group_theory)" title="Descendant tree (group theory)">descendant trees</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Representing_trees">Representing trees</h2></div>

<p>There are many ways of visually representing tree structures.

Almost always, these boil down to variations, or combinations,

of a few basic styles:

</p>

<div class="mw-heading mw-heading3"><h3 id="Classical_node-link_diagrams">Classical node-link diagrams</h3></div>

<p>Classical node-link diagrams, that connect nodes together with line segments:

</p>

<th colspan="3" style="padding:0 0.5em;">encyclopedia

</th></tr>

<tr>

<th colspan="2" style="padding:0 0.5em;">/<br>culture

</th>

<th style="padding:0 0.5em;">\<br>science

</th></tr>

<tr>

<th style="padding:0 0.5em;">/<br>art

</th>

<th style="padding:0 0.5em;">\<br>craft

</th></tr></tbody></table></div>

<div class="mw-heading mw-heading3"><h3 id="Nested_sets">Nested sets</h3></div>

<p><a href="Nested_set_collection" title="Nested set collection"> Nested sets</a> that use enclosure or containment to show parenthood; examples include <a href="Treemapping" title="Treemapping">TreeMaps</a>, fractal maps, and <a href="Euler_diagram" title="Euler diagram">Euler diagrams</a>:

</p>

</th>

<th rowspan="2">encyclopedia

</th></tr>

<tr>

</th>

</th></tr>

<tr>

<th>

</th>

<th rowspan="2">culture

</th></tr>

<tr>

</th>

</th></tr>

<tr>

<th colspan="3" style="border-width:0 1px 1px 1px;border-style:solid;">art   craft

</th></tr></tbody></table>

</th>

<th>science 

</th></tr></tbody></table>

</th></tr></tbody></table></div>

<div class="mw-heading mw-heading3"><h3 id="Layered_"icicle"_diagrams">Layered "icicle" diagrams</h3></div>

<p>Layered "icicle" diagrams that use alignment/adjacency.

</p>

<th colspan="3">encyclopedia

</th></tr>

<tr>

<th colspan="2">culture

</th>

<th>science

</th></tr>

<tr>

<th>art

</th>

<th>craft

</th></tr></tbody></table></div>

<div class="mw-heading mw-heading3"><h3 id="Outlines_and_tree_views">Outlines and tree views</h3></div>

<p>

Lists or diagrams that use indentation, sometimes called "<a href="Outline_(hierarchical)" class="mw-redirect" title="Outline (hierarchical)">outlines</a>" or "<a href="Tree_view" title="Tree view">tree views</a>".

</p><p>An outline:

</p>

<dl><dd><b>encyclopedia</b>

<dl><dd><b>culture</b>

<dd><b>craft</b></dd></dl></dd>

<dd><b>science</b></dd></dl></dd></dl>

</div>

<p>A tree view:

</p>

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<ul><li><b>encyclopedia</b>

<ul><li><b>culture</b>

<li><b>craft</b></li></ul></li>

<li><b>science</b></li></ul></li></ul>

</div>

<div class="mw-heading mw-heading3"><h3 id="Nested_parentheses">Nested parentheses</h3></div>

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</style><div role="note" class="hatnote navigation-not-searchable">See also: <a href="Newick_format" title="Newick format">Newick format</a> and <a href="Dyck_language" title="Dyck language">Dyck language</a></div>

<p>A correspondence to nested parentheses was first noticed by Sir <a href="Arthur_Cayley" title="Arthur Cayley">Arthur Cayley</a>:

</p>

<p><b>((art,craft)culture,science)encyclopedia</b><br>

or<br>

<b>encyclopedia(culture(art,craft),science)</b>

</p>

</div>

<div class="mw-heading mw-heading3"><h3 id="Radial_trees">Radial trees</h3></div>

<div role="note" class="hatnote navigation-not-searchable">See also: <a href="Radial_tree" title="Radial tree">Radial tree</a></div>

<p>Trees can also be <a href="Radial_tree" title="Radial tree">represented radially</a>:

</p>

<th>art<br>      \

</th>

<th>craft<br>/    

</th></tr>

<tr>

<th colspan="2">culture<br>|

</th></tr>

<tr>

<th colspan="2" style="font-size:125%;">encyclopedia

</th></tr>

<tr>

<th colspan="2">|<br>science

</th></tr></tbody></table></div>

<dl><dt>Kinds of trees</dt>

<li><a href="Dancing_tree" title="Dancing tree">Dancing tree</a></li>

<li><a href="Decision_tree" title="Decision tree">Decision tree</a></li>

<li><a href="Left-child_right-sibling_binary_tree" title="Left-child right-sibling binary tree">Left-child right-sibling binary tree</a></li>

<li><a href="Porphyrian_tree" title="Porphyrian tree">Porphyrian tree</a></li>

<li><a href="Tree_(data_structure)" class="mw-redirect" title="Tree (data structure)">Tree (data structure)</a></li>

<li><a href="Tree_(graph_theory)" title="Tree (graph theory)">Tree (graph theory)</a></li>

<li><a href="Tree_(set_theory)" title="Tree (set theory)">Tree (set theory)</a></li></ul>

<dl><dt>Related articles</dt>

<ul><li><a href="Data_drilling" title="Data drilling">Data drilling</a></li>

<li><a href="Hierarchical_model" class="mw-redirect" title="Hierarchical model">Hierarchical model</a>: <a href="Hierarchical_clustering" title="Hierarchical clustering">clustering</a> and <a href="Hierarchical_query" class="mw-redirect" title="Hierarchical query">query</a></li>

<li><a href="Tree_testing" title="Tree testing">Tree testing</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://github.com/ethereum/wiki/wiki/Glossary">"Ethereum Glossary"</a>. <i>GitHub</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190425135357/https://github.com/ethereum/wiki/wiki/Glossary">Archived</a> from the original on 25 April 2019<span class="reference-accessdate">. Retrieved <span class="nowrap">17 April</span> 2019</span>.</cite></span>

</li>

<cite id="CITEREFReference-OED-_tree" class="citation encyclopaedia cs1"><span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://www.oed.com/search/dictionary/?q=tree">"tree"</a></span>. <i><a href="Oxford_English_Dictionary" title="Oxford English Dictionary">Oxford English Dictionary</a></i> (Online ed.). <a href="Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>.</cite> <span style="font-size:0.95em; font-size:95%; color: var( --color-subtle, #555 )">(Subscription or <a rel="nofollow" class="external text" href="https://www.oed.com/public/login/loggingin#withyourlibrary">participating institution membership</a> required.)</span></span>

</li>

<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.w3.org/TR/DOM-Level-2-Core/introduction.html">"What is the Document Object Model?"</a>. <i>W3C Architecture domain</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120212033934/http://www.w3.org/TR/DOM-Level-2-Core/introduction.html">Archived</a> from the original on 2012-02-12<span class="reference-accessdate">. Retrieved <span class="nowrap">2006-12-05</span></span>.</cite></span>

</li>

</ol></div>

<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

<p>Identification of some of the basic styles of tree structures can be found in:

</p>

<ul><li><a href="Jacques_Bertin" title="Jacques Bertin">Jacques Bertin</a>, <i>Semiology of Graphics</i>, 1983, University of Wisconsin Press (2nd edition 1973, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0299090609</bdi>;</li>

<li><cite id="CITEREFDonald_E._Knuth1968" class="citation book cs1"><a href="Donald_E._Knuth" class="mw-redirect" title="Donald E. Knuth">Donald E. Knuth</a> (1968). <i><a href="The_Art_of_Computer_Programming" title="The Art of Computer Programming">The Art of Computer Programming</a></i>. Volume 1: Fundamental Algorithms. Addison-Wesley. pp. <span class="nowrap">309–</span>310.</cite></li>

<li>Brian Johnson and <a href="Ben_Shneiderman" title="Ben Shneiderman">Ben Shneiderman</a>, "<a rel="nofollow" class="external text" href="https://ieeexplore.ieee.org/document/175815">Tree-maps: A space-filling approach to the visualization of hierarchical information structures</a>", in <i>Proceedings of IEEE Visualization (VIS)</i>, 1991, pp. 284–291, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-8186-2245-8</bdi>;</li>

<li><a href="Peter_Eades" title="Peter Eades">Peter Eades</a>, Tao Lin, and Xuemin Lin, "Two Tree Drawing Conventions", <i>International Journal of Computational Geometry and Applications</i>, 1993, volume 3, number 2, pp. 133–153.</li>

<li><cite id="CITEREFManuel_Lima2014" class="citation book cs1"><a href="Manuel_Lima" title="Manuel Lima">Manuel Lima</a> (2014). <i>The Book of Trees: Visualizing Branches of Knowledge</i> (1st ed.). New York: Princeton Architectural Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-616-89218-0</bdi>.</cite></li></ul>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

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<div class="side-box-text plainlist">Wikimedia Commons has media related to <a href="https://commons.wikimedia.org/wiki/Tree_diagram" class="extiw external" title="commons:Tree diagram"><span style="font-style:italic; font-weight:bold;">Tree diagram</span></a>.</div></div>

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<ul><li><a rel="nofollow" class="external text" href="http://www.trex.uqam.ca">Visualization of phylogenetic trees on the T-REX server</a></li>

<li><a rel="nofollow" class="external text" href="http://www.stcwdc.org/PDF/newsletter_may05.pdf">Using a tree structure to design a business process</a> – from the <a href="Society_for_Technical_Communication" title="Society for Technical Communication">Society for Technical Communication</a></li></ul></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2025-08-05" href="https://en.wikipedia.org/wiki/?title=Tree_structure&oldid=1304380904">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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