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A hierarchy (Greek hieros sacred, arkho rule) is a system of rank ing and organizing things. Different fields use the word in slightly different ways, but a particular definition (below) captures the core of almost all uses.

Originally, "hierarchy" meant "rule by priests". Since hierarchical churches such as the Roman Catholic and Eastern Orthodox churches had tables of organization that were "hierarchical" in the modern sense of the word, the term came to refer to similar organizational methods in more general settings.

Examples of hierarchy:

1 General description (informal)

A precise, mathematical definition of hierarchy will be given below. This section will try to explore the ideas behind that more compact definition.

A hierarchy is based on an asymmetrical relationship, such as "is the boss of", "is part of", or "is better than". Such relationships are "asymmetrical" in the sense that if they "work one way", they don't "work the other". For example, if Sally is the boss of Jim, then Jim is not the boss of Sally. When two nodes are related, one is designated the "superior" (or sometimes the "parent") and the other the "subordinate" (or sometimes the "child"). In the intuitive case of the "is the boss of" relation, the boss is the superior and the employee is the subordinate.


Illustration: A hypothetical hierarchical organization for an encyclopedia. Each node "contains" all the sections below it; e.g. the culture section contains the art section and the craft section.

A hierarchy's asymmetrical relationship can link entities in one of three ways: directly, indirectly, or not at all. The illustration shows a direct link between the craft and culture sections; the craft section is directly linked to the culture section by the "contains" relationship. This is akin to how your boss is directly in charge of you. In contrast, the illustration shows an indirect link between craft and encyclopedia; the craft section is only "contained" by the encyclopedia as a whole by virtue of being "contained" by the culture section. This is akin to how the CEO of a company is in charge of a factory worker only via middle management. Finally, there is effectively no link between the art and the craft sections; neither section contains the other. This is akin to two co-workers, neither of whom is the other's boss.

Every member is reachable from any other by following the relationship in either direction, but there is no way of coming back to a particular member by always following the relationship in the same direction.





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