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networks and graph theory

  In human geography the term network is mainly used to refer to a transport network either of permanent facilities (road, rail, canal) or of scheduled services (bus, train, airlines). It has however been extended to cover many other types of line or linkage patterns including administrative boundaries, social contacts (see social network), and telecommunications.

The representation of a network for purposes of description and analysis has been tackled in a number of ways. cartographic representations often required the compiler to discard significant amounts of information in order to portray their salient features. This was taken one step further by using graph theory (a branch of mathematics), which represented the network as a series of nodes (or vertices) and the links (or edges) between them, with each node or vertex having an equal weighting of unity. This was in turn capable of being represented by a binary matrix. Both the graph and the binary matrix were then susceptible to a range of mathematical analyses which identified salient characteristics of the network, but the loss of information (even distortions) occasioned by the reduction of a network to a graph raised doubts about the validity of the approach in geography. The development of high-speed computers and geographical information systems has resolved the problem to some extent, because it is now possible to store and retrieve highly detailed descriptions of networks within such systems without resorting to abstraction, but there remain problems of arriving at satisfactory ways of summarizing that wealth of information.

However the network is represented, a number of characteristics of networks are of importance to geography — density, connectedness, and orientation. Network density (most simply, length of network per unit area) is important because it bears a mathematical and empirical statistical relationship with the average distance of points in an area from their nearest route or node, thus having implications for accessibility. Network connectedness (sometimes referred to as connectivity) identifies whether movements can be made between locations on the network, and how directly such movements may be made. In measuring the latter property, use is made of the ratio between route distance and geodetic distance (often referred to as the route factor): high ratios suggest a poorly connected network, but may also reflect the indirectness of individual routes (for example as a consequence of rugged terrain). Empirical work suggests that route factors are typically higher for rail networks (around 1.8) than for road networks (1.3 to 1.4). Connectedness is usually seen as a characteristic of the whole network, but it may also be seen as a characteristic which differentiates between locations or nodes (some are well-connected to other places, but others are not). It is therefore linked to the third concept — orientation: a network may be structured in such a way that some directions of movement are better served than others so that, for example, a radial network may favour movements to and from a central point in contrast to circumferential movements, while a grid network will favour two directions (the orientation of the grid) against diagonal movements.

In addition to such descriptive and analytic studies geographers have attempted to explain the form of networks. Such explanation may focus on the decisions to construct and maintain individual network elements (ports, airports, road, rail or canal links) or on the way whole network characteristics are associated with other variables (date of construction, political conditions, population density, terrain etc.). (AMH)

Suggested Reading Chorley, R.J. and Haggett, P. 1974: Network analysis in geography, 2nd edn. London: Edward Arnold. New York: St. Martin\'s Press.



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