Hierarchy

A hierarchy (from the Greek hierarkhia, 'rule of a high priest', from hierarkhes, 'president 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. Hierarchy is an important concept in a wide variety of fields, such as philosophy, mathematics, computer science, organizational theory, systems theory, and the social sciences (especially political philosophy). A hierarchy (from the Greek hierarkhia, 'rule of a high priest', from hierarkhes, 'president 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. Hierarchy is an important concept in a wide variety of fields, such as philosophy, mathematics, computer science, organizational theory, systems theory, and the social sciences (especially political philosophy). A hierarchy can link entities either directly or indirectly, and either vertically or diagonally. 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. 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 is one such form. Hierarchies have their own special vocabulary. These terms are easiest to understand when a hierarchy is diagrammed (see below). In an organizational context, the following terms are often used related to hierarchies: In a mathematical context (in graph theory), the general terminology used is different. Most hierarchies use a more specific vocabulary pertaining to their subject, but the idea behind them is the same. For example, with data structures, objects are known as nodes, superiors are called parents and subordinates are called children. In a business setting, a superior is a supervisor/boss and a peer is a colleague. Degree of branching refers to the number of direct subordinates or children an object has (in graph theory, equivalent to the number of other vertices connected to via outgoing arcs, in a directed graph) a node has. Hierarchies can be categorized based on the 'maximum degree', the highest degree present in the system as a whole. Categorization in this way yields two broad classes: linear and branching. In a linear hierarchy, the maximum degree is 1. In other words, all of the objects can be visualized in a line-up, and each object (excluding the top and bottom ones) has exactly one direct subordinate and one direct superior. Note that this is referring to the objects and not the levels; every hierarchy has this property with respect to levels, but normally each level can have an infinite number of objects. An example of a linear hierarchy is the hierarchy of life. In a branching hierarchy, one or more objects has a degree of 2 or more (and therefore the minimum degree is 2 or higher). For many people, the word 'hierarchy' automatically evokes an image of a branching hierarchy. Branching hierarchies are present within numerous systems, including organizations and classification schemes. The broad category of branching hierarchies can be further subdivided based on the degree.