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:
- Object: one entity (e.g., a person, department or concept or element of arrangement or member of a set)
- System: the entire set of objects that are being arranged hierarchically (e.g., an administration)
- Dimension: another word for "system" from on-line analytical processing (e.g. cubes)
- Member: an (element or object) at any (level or rank) in a (class-system, taxonomy or dimension)
- Terms about Positioning
- Rank: the relative value, worth, complexity, power, importance, authority, level etc. of an object
- Level or Tier: a set of objects with the same rank OR importance
- Ordering: the arrangement of the (ranks or levels)
- Hierarchy: the arrangement of a particular set of members into (ranks or levels). Multiple hierarchies are possible per (dimension taxonomy or Classification-system), in which selected levels of the dimension are omitted to flatten the structure
- Terms about Placement
- Hierarch, the apex of the hierarchy, consisting of one single orphan (object or member) in the top level of a dimension. The root of an inverted-tree structure
- Member, a (member or node) in any level of a hierarchy in a dimension to which (superior and subordinate) members are attached
- Orphan, a member in any level of a dimension without a parent member. Often the apex of a disconnected branch. Orphans can be grafted back into the hierarchy by creating a relationship (interaction) with a parent in the immediately superior level
- Leaf, a member in any level of a dimension without subordinates in the hierarchy
- Neighbour: a member adjacent to another member in the same (level or rank). Always a peer.
- Superior: a higher level or an object ranked at a higher level (A parent or an ancestor)
- Subordinate: a lower level or an object ranked at a lower level (A child or a descendent)
- Collection: all of the objects at one level (i.e. Peers)
- Peer: an object with the same rank (and therefore at the same level)
- Interaction: the relationship between an object and its direct superior or subordinate (i.e. a superior/inferior pair)
- a direct interaction occurs when one object is on a level exactly one higher or one lower than the other (i.e., on a tree, the two objects have a line between them)
- Distance: the minimum number of connections between two objects, i.e., one less than the number of objects that need to be "crossed" to trace a path from one object to another
- Span: a qualitative description of the width of a level when diagrammed, i.e., the number of subordinates an object has
- Terms about Nature
- Attribute: a heritable characteristic of (members and their subordinates) in a level (e.g. hair-colour)
- Attribute-value: the specific value of a heritable characteristic (e.g. Auburn)
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
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.
A flat hierarchy is a branching hierarchy in which the maximum degree approaches infinity, i.e., that has a wide span. Most often, systems intuitively regarded as hierarchical have at most a moderate span. Therefore, a flat hierarchy is often not viewed as a hierarchy at all. For example, diamonds and graphite are flat hierarchies of numerous carbon atoms which can be further decomposed into subatomic particles.
An overlapping hierarchy is a branching hierarchy in which at least one object has two parent objects. For example, a graduate student can have two co-supervisors to whom the student reports directly and equally, and who have the same level of authority within the university hierarchy (i.e., they have the same position or tenure status).