| General Network Theory (2009) | |||||||||||||||
Abstract | |||||||||||||||
| complex web-like structures describe a wide variety of systems of high technological and intellectual importance. For example, the cell is best described as a complex network of proteins and small molecules connected by biochemical reactions; the Internet is a complex network of routers and computers linked by various physical or wireless links; fads and ideas spread on the social network whose nodes are human beings and edges represent various social relationships; the World-Wide Web is an enormous virtual network of webpages connected by hyperlinks. A system of elements that interact or regulate each other can be represented by a mathematical object called a graph (Bollobás 1979). Here graph is not used in its usual meaning of ‘diagram of a functional relationship’, but as ‘a collection of nodes and edges’, in other words, a network. At the simplest level, the system’s elements are reduced to graph nodes (also called vertices) and their interactions are reduced to edges connecting pairs of nodes (see Figure 1, overleaf). A graph at its simplest is a connection of nodes (A, B, C…) and edges (AC, BC, CD, CJ…). The node arrangement and length of edges does not matter, only which is connected to which. Edges can be either directed, specifying a source | |||||||||||||||
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