# Hierarchy

A Hierarchy is a tree graph that is a semantic representation that represents isA relations (between nodes).

## References

### 2013

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Hierarchy
• A hierarchy (Greek: hierarchia (ἱεραρχία), from hierarches, "leader of sacred rites") is an arrangement of items (objects, names, values, categories, etc.) in which the items are represented as being "above," "below," or "at the same level as" one another. Abstractly, a hierarchy can be modelled mathematically as a rooted tree: the root of the tree forms the top level, and the children of a given vertex are at the same level, below their common parent.

A hierarchy (sometimes abbreviated HR) can link entities either directly or indirectly, and either vertically or horizontally. The only direct links in a hierarchy, insofar as they are hierarchical, are to one's immediate superior or to one of one's subordinates, although a system that is largely hierarchical can also incorporate alternative hierarchies. Indirect hierarchical links can extend "vertically" upwards or downwards via multiple links in the same direction, following a path. All parts of the hierarchy which are not linked vertically to one another nevertheless can be "horizontally" linked through a path by traveling up the hierarchy to find a common direct or indirect superior, and then down again. This is akin to two co-workers or colleagues; each reports to a common superior, but they have the same relative amount of authority. Organizational forms exist that are both alternative and complementary to hierarchy. Heterarchy (sometimes abbreviated HT) is one such form.

### 2009

• (WordNet, 2009) ⇒ http://wordnetweb.princeton.edu/perl/webwn?s=hierarchy
• S: (n) hierarchy (a series of ordered groupings of people or things within a system) "put honesty first in her hierarchy of values"
• S: (n) hierarchy, power structure, pecking order (the organization of people at different ranks in an administrative body)

• http://en.wiktionary.org/wiki/hierarchy
• Noun
• 1. A body of authoritative officials organized in nested ranks.
• 2. Any group of objects ranked so that every one but the topmost is subordinate to a specified one above it.
• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Hierarchy_(mathematics)
• In mathematics, a hierarchy is a preorder, i.e. an ordered set. The term is used to stress a natural hierarchical relation among the elements. In particular, it is the preferred terminology for posets whose elements are classes of objects of increasing complexity. In that case, the preorder defining the hierarchy is the class-containment relation. Containment hierarchies are thus special cases of hierarchies.