A tree structure 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, even though the chart is generally upside down compared to an actual tree, with the "root" 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 also tree (set theory). Other related pages are listed below.
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Every finite tree structure has a member that has no superior. This member is called the "root" or root node. It can be thought of as the starting node. The converse is not true: infinite tree structures may or may not have a root node.
The lines connecting elements are called "branches", the elements themselves are called "nodes". Nodes without children are called leaf nodes, "end-nodes", or "leaves".
The names of relationships between nodes are modeled after family relations. The gender-neutral names "parent" and "child" have largely displaced the older "father" and "son" terminology, although the term "uncle" is still used for other nodes at the same level as the parent.
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", being the root of the tree, is the ancestor of "science", "culture", "art" and "craft". Finally, "science", "art" and "craft", being leaves, are ancestors of no other node.
Tree structures are used to 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.
In a tree structure there is one and only one path from any point to any other point.
Tree structures are used extensively in computer science (see Tree (data structure) and telecommunications.)
For a formal definition see set theory.
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:
encyclopedia
/ \
science culture
/ \
art craft
Nested sets that use enclosure/containment to show parenthood, examples include TreeMaps and fractal maps:
+------encyclopedia------+
| +--culture--+ |
| science |art craft| |
| +-----------+ |
+------------------------+
Layered "icicle" diagrams that use alignment/adjacency:
+-------------------+
| encyclopedia |
+---------+---------+
| science | culture |
+---------+---+-----+
|art|craft|
+---+-----+
Lists or diagrams that use indentation, sometimes called "outlines" or "tree views":
encyclopedia
science
culture
art
craft
A correspondence to nested parentheses was first noticed by Sir Arthur Cayley.
(science,(art,craft)culture)encyclopedia
or:
encyclopedia(culture(art,craft),science)
Also, trees can be represented radially.
Identification of some of the basic styles of tree structures can be found in: