A heterarchy may be parallel to a hierarchy, subsumed to a hierarchy, or it may contain hierarchies; the two kinds of structure are not mutually exclusive. In fact, each level in a hierarchical system is composed of a potentially heterarchical group which contains its constituent elements.
In a group of related items, heterarchy is a state wherein any pair of items is likely to be related in two or more differing ways. Whereas hierarchies sort groups into progressively smaller categories and subcategories, heterarchies divide and unite groups variously, according to multiple concerns that emerge or recede from view according to perspective. Crucially, no one way of dividing a heterarchical system can ever be a totalizing or all-encompassing view of the system, each division is clearly partial, and in many cases, a partial division leads us, as perceivers, to a feeling of contradiction that invites a new way of dividing things. (But of course the next view is just as partial and temporary.) Heterarchy is a name for this state of affairs, and a description of a heterarchy usually requires ambivalent thought...a willingness to ambulate freely between unrelated perspectives.
Numerous observers in the information sciences have argued that heterarchical structure processes more information more effectively than hierarchical design. An example of the potential effectiveness of heterarchy would be the rapid growth of the heterarchical Wikipedia project in comparison with the failed growth of the Nupedia project. Heterarchy increasingly trumps hierarchy as complexity and rate of change increase.
Informational heterarchy can be defined as an organizational form somewhere between hierarchy and network that provides horizontal links that permit different elements of an organization to cooperate whilst individually optimizing different success criteria. In an organizational context the value of heterarchy derives from the way in which it permits the legitimate valuation of multiple skills, types of knowledge or working styles without privileging one over the other. In information science, therefore, heterarchy, responsible autonomy and hierarchy are sometimes combined under the umbrella term Triarchy.
This concept has also been applied to the field of archaeology, where it has enabled researchers to better understand social complexity. For further reading see the works of Carole Crumley.
In Bondarenko (2005), heterarchy is defined as "the relation of elements to one another when they are unranked or when they possess the potential for being ranked in a number of different ways") and is therefore not strictly the opposite of hierarchy, but is rather the opposite of homoarchy (defined as "the relation of elements to one another when they possess the potential for being ranked in one way only" (Bondarenko, Grinin, Korotayev 2002: 55)).
Political hierarchies and heterarchies are systems in which multiple dynamic power structures govern the actions of the system. They represent different types of network structures that allow differing degrees of connectivity. In a (tree-structured) hierarchy every node is connected to at most one parent node and zero or more child nodes. In a heterarchy, however, a node can be connected to any of its surrounding nodes without needing to go through or get permission from some other node.
Socially, a heterarchy distributes privilege and decision-making among participants, while a hierarchy assigns more power and privilege to the members high in the structure. In a systemic perspective, Gilbert Probst, Jean-Yves Mercier and al. (1992) describe heterarchy as the flexibility of the formal relationships inside an organization. Domination and subordination links can be reversed and privileges can be redistributed in each situation, following the needs of the system.
A heterarchical network could be used to describe neuron connections or democracy, although there are clearly hierarchical elements in both.