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.
In plain English, a hierarchy can be thought of as a set in which:
1. No element is superior to itself, and
2. One element, the hierarch, is superior to all of the other elements in the set.
The first requirement is also interpreted to mean that a hierarchy can have no circular relationships; the association between two objects is always transitive. The second requirement asserts that a hierarchy must have a leader or root that is common to all of the objects.