Cities as Small Worlds

Years ago, Stanley Milgram (1967) in a far-sighted discussion of social structure suggested that everyone on the planet was probably connected to everybody else by no more than `six degrees of separation'. He illustrated his thesis with an experiment which showed that randomly selected individuals in Kansas and Nebraska could, on average, reach two purposefully selected individuals in the Boston area by no more than five intermediaries, making six links in all in this particular social network. He called this phenomenon `the small world' problem. For thirty years, this idea remained a curiosity, easy to understand but hard to theorize about other than in the most speculative fashion. But suddenly there is flurry of work, emanating not from social science but from complexity theory and statistical physics which seeks to argue that most networks in nature as well as society, are `small worlds'önetworks which display strong connectivity and clustering at the local level but with significant links at the global (Watts, 1999). In graph theory, a small world is a network which is composed of clusters of nodes which are locally linked in the manner of a grid say, but which also has links which span the entire graph, thus binding the furthest members of the collective together. If the graph were merely composed of adjacent links like a grid, then the index of clustering measuring the local density would be high, but the average distance from any node to any other would be long. In a network whose links appear randomly configured, the average distance would be lower but the clustering index would be low too. Small worlds are graphs where the clustering index is high and the average distance is low. In short, small worlds are the best of all worlds, with short local distances where you can reach a large number of adjacent members quickly and small average distances which enable you reach any member of the collective quickly too. This might be likened to living in a densely connected local group but having the ability to hop quickly between distant members using long-distance ties and then descending to interact with members of any locality by using their dense local network. In spatial terms, cities and systems of cities would appear to be prime candidates. Most small world research has treated the network as a static, aspatial, or topological structure, showing that such networks appear in many different contexts, and defining processes of change that take place within them.Watts (1999) illustrates that networks of connections between movie actors, regional power networks, and the nervous system of the earthworm are `small worlds' implying that, to work efficiently, locally higher densities and global connectivity must be in place. He also shows that by taking a local network with high clustering and rewiring it, gradually introducing long-range links, a distinct regime, reminiscent of a phase transition, appears where the network takes on the small world quality, before it eventually transforms to a random graph. Processes working across such networks are even more suggestive of their small worldliness. Consider the recent foot and mouth epidemic in Britain. Most policy to stop the disease spreading was designed on the assumption that it was spread locally from cluster to cluster, and thus slowly. However, it was soon discovered that, beside high-density local clusters, there were stronger, longer distance ties relating to markets.When a flock of sheep with the disease appeared in northern France, it became clear that large-scale movements within the industry were responsible for its rapid spread, indicating that the contact network for such disease transmission is more like a `small' than a `local' world. Editorial Environment and Planning B: Planning and Design 2001, volume 28, pages 637 ^ 638