# 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
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 .