Description
Several kinds of network analysis have been developed for different problem areas. In each case there is considerable dependence on graph theory (described separately), but other techniques may also be used, depending on the extent to which the network's characteristics are quantifiable.
1. Circuit analysis: In the analysis of electrical and electronic circuits (composed of resistors, inductors, and capacitors), the central problem of network analysis is to find expressions for the node-pair potentials and branch currents at various points of interest in the circuit, and to determine the behaviour of the over-all network with respect to specified terminals.
2. Flow-handling networks in general: Road networks, power grids, airline routes, railroad networks, pipeline networks and other networks through which commodities flow, use a form of network analysis 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. This involves problems of economics and logistics and makes use of the techniques of linear programming, queuing theory, and probability theory as a form of systems analysis.
3. Project planning: This technique (described separately) is based on the representation of the component activities of a project as the relationships in a network, with the nodes representing the start and completion points. The analysis is used as an aid to work scheduling, particularly in the event of delays or where problems of resource allocation arise.
4. Citation analysis: 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: 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.
6. Social network analysis: In an effort to analyze 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, proposals have been made for the use of topology (from which graph theory is derived), algebraic topology, tensor calculus, matrix analysis, and lattice theory.