tree structure

The tree elements are called "nodes".

The lines connecting elements are called "branches".

Nodes without children are called leaf nodes, "end-nodes", or "leaves".

Every finite tree structure has a member that has no superior. This member is called the "root" or root node. The root is the starting node. But the converse is not true: infinite tree structures may or may not have a root node.

The names of relationships between nodes model the kinship terminology 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".{{cite web |title=Ethereum Glossary |url=https://github.com/ethereum/wiki/wiki/Glossary |website=GitHub |access-date=17 April 2019 |archive-date=25 April 2019 |archive-url=https://web.archive.org/web/20190425135357/https://github.com/ethereum/wiki/wiki/Glossary |url-status=live }}

• 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.
• "Sibling" ("brother" or "sister") nodes share the same parent node.
• A node's "uncles" (sometimes "ommers") are siblings of that node's parent.
• 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.

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.

Tree structures can depict all kinds of taxonomic knowledge, such as family trees, the biological evolutionary tree, the evolutionary tree of a language family, the grammatical structure 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, mathematical trees of integer sets, et cetera.

The Oxford English Dictionary records use of both the terms "tree structure" and "tree-diagram" from 1965 in Noam Chomsky's Aspects of the Theory of Syntax.

{{OED | tree}}

In a tree structure there is one and only one path from any point to any other point.

Computer science uses tree structures extensively (see Tree (data structure) and telecommunications.)

For a formal definition see set theory, and for a generalization in which children are not necessarily successors, see prefix order.

File:Tree Map.png as a nested set ]]

File:1934-Thermionic-Tube-Chart.jpg

• Internet:
• usenet hierarchy
• Document Object Model's logical structure,{{cite web |url=http://www.w3.org/TR/DOM-Level-2-Core/introduction.html |title=What is the Document Object Model? |access-date=2006-12-05 |work=W3C Architecture domain |archive-date=2012-02-12 |archive-url=https://web.archive.org/web/20120212033934/http://www.w3.org/TR/DOM-Level-2-Core/introduction.html |url-status=live }} Yahoo! subject index, Curlie
• Operating system: directory structure
• Information management: Dewey Decimal System, PSH, this hierarchical bulleted list
• Management: hierarchical organizational structures
• Computer science:
• binary search tree
• red–black tree
• AVL tree
• R-tree
• doubly logarithmic tree
• Biology: evolutionary tree
• Business: pyramid selling scheme
• Project management: work breakdown structure
• Linguistics:
• (Syntax) Phrase structure trees
• (Historical Linguistics) Tree model of language change
• Sports: business chess, playoffs brackets
• Mathematics: Von Neumann universe
• Group theory: descendant trees

There are many ways of visually representing tree structures.

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

of a few basic styles:

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

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Nested sets that use enclosure or containment to show parenthood; examples include TreeMaps, fractal maps, and Euler diagrams:

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Layered "icicle" diagrams that use alignment/adjacency.

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{{anchor|Outlines|Tree views}}

Lists or diagrams that use indentation, sometimes called "outlines" or "tree views".

An outline:

{{clear}}

A tree view:

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{{clear right}}

{{See also|Newick format|Dyck language}}

A correspondence to nested parentheses was first noticed by Sir Arthur Cayley:

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{{See also|Radial tree}}

Trees can also be represented radially:

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;Kinds of trees:

• B-tree
• Dancing tree
• Decision tree
• Left-child right-sibling binary tree
• Porphyrian tree
• Tree (data structure)
• Tree (graph theory)
• Tree (set theory)

;Related articles:

• Data drilling
• Hierarchical model: clustering and query
• Tree testing

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

• Jacques Bertin, Semiology of Graphics, 1983, University of Wisconsin Press (2nd edition 1973, {{ISBN|978-0299090609}};
• {{cite book |author=Donald E. Knuth |title=The Art of Computer Programming |series=Volume 1: Fundamental Algorithms |year=1968 |publisher=Addison-Wesley |pages=309–310}}
• Brian Johnson and Ben Shneiderman, "[https://ieeexplore.ieee.org/document/175815 Tree-maps: A space-filling approach to the visualization of hierarchical information structures]", in Proceedings of IEEE Visualization (VIS), 1991, pp. 284–291, {{ISBN|0-8186-2245-8}};
• Peter Eades, Tao Lin, and Xuemin Lin, "Two Tree Drawing Conventions", International Journal of Computational Geometry and Applications, 1993, volume 3, number 2, pp. 133–153.
• {{cite book |author1=Manuel Lima |author1-link=Manuel Lima |title=The Book of Trees: Visualizing Branches of Knowledge|date=2014 |publisher=Princeton Architectural Press |location=New York |isbn=978-1-616-89218-0 |edition=1st}}

{{Commons|Tree diagram}}

• [http://www.trex.uqam.ca Visualization of phylogenetic trees on the T-REX server]
• [http://www.stcwdc.org/PDF/newsletter_may05.pdf Using a tree structure to design a business process] – from the Society for Technical Communication

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Category:Trees (data structures)

Category:Conceptual models

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