Hierarchy

1. A system composed of interrelated subsystems, each of the subsystems being in turn hierarchic in structure until the lowest level of elementary subsystem is reached. Hierarchic systems have some common properties that are independent of their specific content. Such systems are nearly decomposable, namely interactions among subsystems are relatively weak compared with interactions within subsystems. Complex systems frequently take the form of hierarchy and tend to evolve more quickly when hierarchically organized. Hierarchical structure and combination into systems of ever higher order is characteristic of reality as a whole and of fundamental importance especially in biology, psychology, and sociology.

2. Hierarchy is the most conspicuous part of the formal structure of any social organization. (As such, it has frequently been falsely identified with the totality of formal structure, and the adjustment of hierarchic relationships has been falsely identified with the totality of the administrative process). The essence of hierarchy is then the distinction between the role of superior expected to exercise authority over one or more subordinates, who in turn function as superiors with respect to a lower level of subordinates.

3. Hierarchic organization is an essential feature of stable complex systems, whether they are inanimate systems, living organisms, social organizations, or patterns of behaviour. As a tree structure, hierarchies may serve to represent evolution as a process, and its projection in taxonomic systems; it may equally represent the step-wise differentiation in embryonic development; it may serve as a structural diagram of the parts-within-parts architecture of organisms or galaxies; or as a functional schema for the analysis of instinctive behaviour by ethologists; or of the phrase-generating machinery by the psycholinguist.

4. A set of things graded in levels by asymmetrical relations. Hierarchies are of many types: social, psychological, linguistic, conceptual, genetic, historical, etc. Structural hierarchies are composed of objects classified by spatial whole/part relations and may include inorganic hierarchies (from atoms to galaxies) or organic hierarchies (from atoms to communities). A free hierarchy is one in which there is no progressive transfer of energy between the levels, and the existence of the system does not impose additional constraints, characteristic of the level, on the degrees of freedom of its parts. A control hierarchy is a heterogeneous structural hierarchy in which causal levels are not separable and there is a progressive transfer of energy between the levels, with each higher level imposing additional constraints on the degrees of freedom of its parts.