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A tree structure, tree diagram, or tree model is a way of representing the hierarchical nature of a structure in a graphical form. It is named a "tree structure" because the classic representation resembles a tree, although the chart is generally upside down compared to a biological tree, with the "stem" at the top and the "leaves" at the bottom.
A tree structure is conceptual, and appears in several forms. For a discussion of tree structures in specific fields, see Tree (data structure) for computer science; insofar as it relates to graph theory, see tree (graph theory) or tree (set theory). Other related articles are listed below.
Terminology and properties
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".
- 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.
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.
Examples of tree structures
- Internet:
- usenet hierarchy
- Document Object Model's logical structure,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
Representing 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
Classical node-link diagrams, that connect nodes together with line segments:
| encyclopedia | ||
|---|---|---|
| / culture | \ science | |
| / art | \ craft | |
Nested sets
Nested sets that use enclosure or containment to show parenthood; examples include TreeMaps, , and Euler diagrams:
 | encyclopedia | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| | | ||||||||||
| |||||||||||
Layered "icicle" diagrams
Layered "icicle" diagrams that use alignment/adjacency.
| encyclopedia | ||
|---|---|---|
| culture | science | |
| art | craft | |
Outlines and tree views
Lists or diagrams that use indentation, sometimes called "outlines" or "tree views".
An outline:
- encyclopedia
- culture
- art
- craft
- science
- culture
A tree view:
- encyclopedia
- culture
- art
- craft
- science
- culture
Nested parentheses
A correspondence to nested parentheses was first noticed by Sir Arthur Cayley:
((art,craft)culture,science)encyclopedia
or
encyclopedia(culture(art,craft),science)
Radial trees
Trees can also be represented radially:
| art \ | craft / |
|---|---|
| culture | | |
| encyclopedia | |
| | science | |
See also
- 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
References
- "Ethereum Glossary". GitHub. Archived from the original on 25 April 2019. Retrieved 17 April 2019.
- "tree". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)
- "What is the Document Object Model?". W3C Architecture domain. Archived from the original on 2012-02-12. Retrieved 2006-12-05.
Further reading
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;
- Donald E. Knuth (1968). The Art of Computer Programming. Volume 1: Fundamental Algorithms. Addison-Wesley. pp. 309–310.
- Brian Johnson and Ben Shneiderman, "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.
- Manuel Lima (2014). The Book of Trees: Visualizing Branches of Knowledge (1st ed.). New York: Princeton Architectural Press. ISBN 978-1-616-89218-0.
External links
- Visualization of phylogenetic trees on the T-REX server
- Using a tree structure to design a business process – from the Society for Technical Communication
This article includes a list of general references but it lacks sufficient corresponding inline citations Please help to improve this article by introducing more precise citations July 2014 Learn how and when to remove this message A tree structure tree diagram or tree model is a way of representing the hierarchical nature of a structure in a graphical form It is named a tree structure because the classic representation resembles a tree although the chart is generally upside down compared to a biological tree with the stem at the top and the leaves at the bottom A tree structure showing the possible hierarchical organization of an encyclopediaThe original Encyclopedie 1752 used a tree diagram to show the way in which its subjects were ordered A tree structure is conceptual and appears in several forms For a discussion of tree structures in specific fields see Tree data structure for computer science insofar as it relates to graph theory see tree graph theory or tree set theory Other related articles are listed below Terminology and propertiesThe 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 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 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 Examples of tree structuresA tree map used to represent a directory structure as a nested setA diagram in the shape of a tree illustrating the evolution of thermionic tubes a type of vacuum tube between 1883 and 1934Internet usenet hierarchy Document Object Model s logical structure 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 treesRepresenting treesThere 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 Classical node link diagrams that connect nodes together with line segments encyclopedia culture science art craft Nested sets Nested sets that use enclosure or containment to show parenthood examples include TreeMaps and Euler diagrams encyclopediacultureart craft science Layered icicle diagrams Layered icicle diagrams that use alignment adjacency encyclopediaculture scienceart craft Outlines and tree views Lists or diagrams that use indentation sometimes called outlines or tree views An outline encyclopediacultureart craft dd science dd A tree view encyclopedia culture art craft science Nested parentheses A correspondence to nested parentheses was first noticed by Sir Arthur Cayley art craft culture science encyclopedia or encyclopedia culture art craft science Radial trees Trees can also be represented radially art craft culture encyclopedia scienceSee alsoKinds of treesB tree Dancing tree Decision tree Left child right sibling binary tree Porphyrian tree Tree data structure Tree graph theory Tree set theory Related articlesData drilling Hierarchical model clustering and query Tree testingReferences Ethereum Glossary GitHub Archived from the original on 25 April 2019 Retrieved 17 April 2019 tree Oxford English Dictionary Online ed Oxford University Press Subscription or participating institution membership required What is the Document Object Model W3C Architecture domain Archived from the original on 2012 02 12 Retrieved 2006 12 05 Further readingIdentification 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 Donald E Knuth 1968 The Art of Computer Programming Volume 1 Fundamental Algorithms Addison Wesley pp 309 310 Brian Johnson and Ben Shneiderman 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 Manuel Lima 2014 The Book of Trees Visualizing Branches of Knowledge 1st ed New York Princeton Architectural Press ISBN 978 1 616 89218 0 External linksWikimedia Commons has media related to Tree diagram Visualization of phylogenetic trees on the T REX server Using a tree structure to design a business process from the Society for Technical Communication
