Tree diagram

Example of a mathematical tree diagram: Pulling from an urn without putting the balls back

A tree diagram (also: tree graph , stemma , branch diagram ) is a graphic representation that shows the relationships between individual elements of a network (i.e. their relationship or hierarchical dependencies) using connecting lines. The name is derived from the ramified structure of these representations.

A distinction is made depending on the area of ​​application:

family tree

shows the chronological order of individual related elements

Decision tree

shows the various possible results of a certain sequence of hierarchical decisions and is mostly used in addition to or in preparation for the decision table

Mind map

shows synoptically the references of different categories of terms or associations to a certain generic term

Cladogram

shows the relationship structure of various systematically named living beings ( taxa )

Phylogenetic tree

shows the relationship structure of different living things in relation to their gene structure

Structure tree

to break down a sentence or text into its components (also: phrase structure diagram ).

A special form of the tree diagram is the dendrogram in which in addition to the number of branches and the length and / or thickness of the edges (which are the connecting lines between the individual node elements of the network called) as characterizing parameters is used. An example of this are the phylogenetic trees , with which the long-term population dynamics are represented in the theory of evolution .

In graph theory , these different types are summarized under the term tree and their individual properties are examined theoretically. See also the article Tree (data structure) .

Tree diagrams are also used in probability calculations to represent multi-level random experiments , for example in urn models .

literature

• Manuel Lima : The Book of Trees: Visualizing Branches of Knowledge. Foreword by Ben Shneiderman . New York: Princeton Architectural Press, 2014 ISBN 978-1-61689-218-0 .

Web links

Commons : Tree diagram  - collection of images, videos and audio files

Wiktionary: Tree diagram  - explanations of meanings, word origins, synonyms, translations

Wikibooks: ${\displaystyle {\begin{smallmatrix}{\mathbf {MATHE} \mu \alpha T\mathbb {R} ix}\end{smallmatrix}}}$  - Mathematics for school

• Linguistic Tree Constructor
• TreeForm Syntax Tree Drawing Software (requires Apple Quicktime)
• phpSyntaxTree - Draw tree diagrams online
• phpSyntaxTree (Unicode) - Draw tree diagrams online (version with Unicode support)
• Probability trees - Draw tree diagrams of any size including probabilities
• Macro for Calc - A StarOffice Basic macro that calculates a probability tree in StarOfficeCalc .