Topology is a branch of geometrical mathematics which is concerned with order, contiguity and relative position, rather than with actual linear dimensions. It is sometimes referred to as 'the rubber sheet geometry', since a pattern on such a sheet can be deformed, yet points on it remain in the same order or relationship; in point of fact the scope of topology is really much wider than this. In contrast to a topographical map, which retains the familiar scale and orientation, a topological map, whilst retaining contiguity of relationships (such as boundaries, relative positions of towns, etc.), uses other criteria (area, annual precipitation, density of population, per capita income, communications systems, etc.) to determine the scale, that is, the information is subjected to a topological transformation. Such a diagrammatic map may clearly bring out novel relationships and patterns. For example, a topological map is seen in every London Underground train compartment, showing the correct sequence of stations, though not to scale and only diagrammatically orientated....

...In more complex topological maps, systems of nodes (i.e. 'zero dimensional' points and dots), arcs ('single dimensional' lines) and regions (two-dimensional surfaces or spaces) are used to construct networks and inter-relationships of immense significance.¹ The linking of arcs will produce networks of various kinds, and the construction and analysis of network models (in terms of what is known as graph theory) is making an important contribution to locational theory.²