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Considerations about Networks and their Classification

By on June 15, 2010

A network is a set of items, which we will call vertices or sometimes nodes, with connections between them, called edges. The study of networks, in the form of mathematical graph theory, is one of the fundamental pillars of discrete mathematics.

Recent years however have witnessed a substantial new movement in network research. This new approach has been driven largely by the availability of computers and communication networks that allow us to gather and analyze data on a scale far larger than previously possible.

A social network is a set of people or groups of people with some pattern of contacts or interactions between them. The patterns of friendships between individuals, business relationships between companies, and intermarriages between families are all examples of networks that have been studied.

 Our second network category is what we call in-formation networks.  A very important example of an information network is the World Wide Web, which is a network of Web pages containing information, linked conjointly by hyperlinks from one page to another. The Web should not be confused with the Internet, which is a physical network of computers linked together by optical fiber and other data connections. Unlike a citation network, the World Wide Web is cyclic; there is no natural ordering of sites and no constraints that prevent the appearance of closed loops. The Web has been very heavily studied since its first appearance in the early 1990s.

The third class of networks is technological networks, man-made networks designed typically for distribution of some commodity or resource, such as electricity or information. The electric power grid is a good example.

A number of biological systems can be usefully delineated as networks. Perhaps the classic example of a biological network is the network of metabolic pathways, which is a mental representation of metabolic substrates and products with directed edges joining them if a known metabolic reaction exists that acts on a given substrate and produces a given product.

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