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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.
The height of the root is the height of the tree. The depth of a node is the length of the path to its root (i.e., its root path). Thus the root node has depth zero, leaf nodes have height zero, and a tree with only a single node (hence both a root and leaf) has depth and height zero.
The height of the tree is the height of the root. The depth of a vertex is the length of the path to its root (root path). The depth of a tree is the maximum depth of any vertex. Depth is commonly needed in the manipulation of the various self-balancing trees, AVL trees in particular. The root has depth zero, leaves have height zero, and a tree ...
Tree topology, a topology based on a hierarchy of nodes in a computer network; Tree diagram (physics), an acyclic Feynman diagram, pictorial representations of the mathematical expressions governing the behavior of subatomic particles; Outliners, a common software application that is used to generate tree diagrams; Network diagram; Tree ...
1. This is the depth of a node plus 1, although some [12] define it instead to be synonym of depth. A node's level in a rooted tree is the number of nodes in the path from the root to the node. For instance, the root has level 1 and any one of its adjacent nodes has level 2. 2. A set of all node having the same level or depth. [12] line
The term arborescence comes from French. [6] Some authors object to it on grounds that it is cumbersome to spell. [7] There is a large number of synonyms for arborescence in graph theory, including directed rooted tree, [3] [7] out-arborescence, [8] out-tree, [9] and even branching being used to denote the same concept. [9]
For infinite trees, simple algorithms often fail this. For example, given a binary tree of infinite depth, a depth-first search will go down one side (by convention the left side) of the tree, never visiting the rest, and indeed an in-order or post-order traversal will never visit any nodes, as it has not reached a leaf (and in fact never will ...
In convex treemaps, the aspect ratio cannot be constant - it grows with the depth of the tree. To attain a constant aspect-ratio, Orthoconvex treemaps [ 17 ] can be used. There, all regions are orthoconvex rectilinear polygons with aspect ratio at most 64; and the leaves are either rectangles with aspect ratio at most 8, or L-shapes or S-shapes ...