Working with networks, where a network is 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 are 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 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 the points. Network synthesis is a branch of the theory of electric networks used to combine together possible elements of a network in the process of designing circuits with required characteristics.
Several kinds of network analysis have been developed for different problem areas, including: 1. Circuit analysis of electrical and electronic circuits (composed of resistors, inductors, and capacitors); 2. Flow-handling networks in general (road networks, power grids, airline routes, railroad networks, pipeline networks and other networks through which commodities flow), to determine maximum flows in networks; the vulnerability of a network to disruption; and the necessary characteristics of the network elements for the required performance; 3. Project planning, in which the component activities of a project are represented as the relationships in a network, with the nodes representing the start and completion points, as an aid to work scheduling, particularly in the event of delays or where problems of resource allocation arise; 4. Citation analysis, where each document published constitutes a node in an extensive network in which the relationships to a given document are the citations of it in other documents. Such networks may be analysed to locate key documents (authors, journals, or research institutes) and the relationships between them as a guide to resource allocation and to an understanding of the history of ideas; 5. Sociometry, where the network is usually severely restricted in content to the friendship or leadership relationships in a relatively small group of people. Such techniques have also been applied to inter-organizational relationships (such as in a community) in order to locate the opinion-forming bodies and the manner in which the community may be influenced with a minimum of effort; and 6. Social network analysis, used to analyse more general social networks, in which there may be several kinds of relationship between several kinds of social entity at several different levels, and including relationships of the entity to itself.