A hierarchy (in Greek: Ιεραρχία, it is derived from ιερός-hieros, sacred, and άρχω-arkho, rule) is a system of ranking and organizing things or people, where each element of the system (except for the top element) is subordinate to a single other element.
The first use of the word "hierarchy" cited by the Oxford English Dictionary was in 1380, when it was used in reference to the three orders of three angels as depicted by Pseudo-Dionysius the Areopagite. Ps.-Dionysius used the word both in reference to the heavenly hierarchy and the ecclesiastical hierarchy [1]. This was the origin of the common meaning of "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 (traditionally with God as the pinnacle of the hierarchy), the term came to refer to similar organizational methods in more general settings.
A hierarchy can link entities either directly or indirectly, and either vertically or horizontally. The only direct links in a hierarchy are to one's immediate superior, or to one of one's subordinates. However, indirect links can extend "vertically" upwards or downwards via multiple links in the same direction. All parts of the hierarchy which are not vertically linked to one another can nevertheless be "horizontally" linked by travelling up the hierarchy to find a common direct or indirect superior, and then down again. This is akin to two co-workers, neither of whom is the other's boss, but both of whose chains of command will eventually meet.
These relationships can be formalized mathematically;
The first use of the word "hierarchy" cited by the Oxford English Dictionary was in 1380, when it was used in reference to the three orders of three angels as depicted by Pseudo-Dionysius the Areopagite. Ps.-Dionysius used the word both in reference to the heavenly hierarchy and the ecclesiastical hierarchy [1]. This was the origin of the common meaning of "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 (traditionally with God as the pinnacle of the hierarchy), the term came to refer to similar organizational methods in more general settings.
A hierarchy can link entities either directly or indirectly, and either vertically or horizontally. The only direct links in a hierarchy are to one's immediate superior, or to one of one's subordinates. However, indirect links can extend "vertically" upwards or downwards via multiple links in the same direction. All parts of the hierarchy which are not vertically linked to one another can nevertheless be "horizontally" linked by travelling up the hierarchy to find a common direct or indirect superior, and then down again. This is akin to two co-workers, neither of whom is the other's boss, but both of whose chains of command will eventually meet.
These relationships can be formalized mathematically;