A group of elements which may be partially or completely interconnected. The connections (termed branches or arcs) can represent roads, power lines, airline routes, information flows, predator-prey relationships in an ecosystem, logical relationships, functional relationships, or the generalized channels through which commodities flow. The elements (termed points or nodes) can represent individuals, communities, power stations, airline terminals, water reservoirs, libraries, organizations, namely any point where a flow or relationship of some kind originates, or terminates. In a more general case, the elements or points in the network may themselves be subnetworks composed of combinations of other kinds of elements.
The characteristics of the network's elements and relationships can be described by values, which may or may not be quantitative. The values can be fixed or they can vary in some way with time. Thus the relationship between two points may not exist during a particular period of time (as in an electrical circuit), or several possible relationship paths may exist between two points (as in a telephone circuit). Different types of relationship may exist between the same two points.
Network analysis (described separately) is used to determine the structure and characteristics of networks. Network synthesis (described separately) is used to combine together possible elements of a network in the process of designing circuits with required characteristics. Network is frequently used as a synonym for system, although systems analysis necessitates quantitative information whereas much analysis of networks can be performed using only information on the existence (or not) of relationships between points.
Some simple structural properties of networks (or parts of networks) using the methods of graph theory (described separately) are given below. More complex methods of network analysis (described separately) exist or are being explored, particularly with a view to analysing complex networks and determining their properties as a whole.
1. Centrality: A measure of the extent to which a given entity is directly or indirectly related to other entities, or isolated from them.
2. Coherence: A measure of the degree of interconnectedness or density of a group of entities. This may be an indication of the degree of development of a group of entities.
3. Range: A measure of the number of other entities to which a particular entity is directly related.
4. Content: The nature or reason for the existence of a relationship between entities. Simple networks can have only one link between two entities. More complex networks may have two or more such links, possibly each of different content.
5. Directedness: A relationship between two entities may have some direction (P to Q or Q to P) or asymmetry, which may be of different types.
6. Durability: A measure of the period over which a certain relationship between entities is activated and used.
7. Intensity: A measure of the strength of the relationship between two entities. (The link from P to Q may be strong, and that from Q to P weak).
8. Frequency: The frequency with which a link is established or cut off, if this is the case.
9. Rearrangeability and Blocking: A network is rearrangeable if alternative paths can be found to link any pair of entities by rearranging the links between other entities. A network is in a blocking state if some pair of entities cannot be connected.