Cities are emergent networks in at least three senses: as dense collections of buildings linked by a network of space; as functional networks formed from the movement of people, goods, and communications; and as social networks of interactions between individuals, groups, and institutions. All three are of interest in themselves, but, from the point of view of understanding cities and the societies that inhabit them, the key theoretical questions are about interactions between them. Is the spatial network in any well-defined sense the by-product of the functional and social network unfolding in space? Is there any sense in which the spatial network aids and abets the emergence of the functional or social networks? Is there any sense in which the spatial and functional networks sponsor the emergence of the distinctive kinds of networks we think of as “urban” societies?
Classical mathematical approaches to these questions have tended to postulate simple linkages between networks, such as the cost of transporting goods over distance to link the spatial and functional networks. These have led to paradigms that conceptualize the city as points in a Euclidean metric field, and so background the non-Euclidean space-time networks that form the raw material of the city. Here we outline a network approach to these questions, using space syntax to address the three kinds of networks in turn. First we address the network of space itself and its origins, and show how the distinctive kinds of spatial networks we find in cities, and the fractal properties we find in them, emerge from the act of building the physical city through the operation of simple mathematical laws that link the placing and shaping of objects to the resulting configuration of ambient space.
We then address the functional network, and show that the primary determinant of movement flows is the emergent configuration of the spatial network itself, and in particular its geometric and topological, rather than metric, properties. This sets in motion the processes by which the spatial network acquires a functional network and so turns collections of building into living cities. We then address the social network and suggest that social networks are peculiar in that in addition to statistical and structural properties they also have the property of being reflexive, in that a certain proportion of their activity is directed at reproducing the structure of the network itself. Since all social systems are nonlocal, and so must overcome space in order to exist, the analysis of the form of reflexivity allows us to show how time and space are internalized into the constitution of social systems. From this platform we can begin to see how and why societies tend to change their form as the initial spatial conditions change from dispersed to concentrated, or vice versa.