A topological analysis of growth in the Zurich road network.

The functioning of a city depends upon physical structures and services. Over time, a city evolves and the layout of its infrastructure is altered, providing a new arrangement of services for citizens. When designing road infrastructure, planners usually add or change existing roads, looking only at local consequences and ignoring the effects on the whole system. This results in an infrastructure that is developed without a clear understanding of how those alterations affect the global topology. We studied the development of road infrastructure in Zurich, Switzerland, modelled as a network. Our objectives were to 1) assess how non-spatial network topological metrics can identify changes in infrastructure over time and 2) determine any patterns of change in the spatial distribution of those metrics. We analyzed three types of betweenness centrality (BC) metrics with different weighting methods that depended upon structural properties, distance, and population distribution within the urban area. The study resulted in four main findings. First, the number of nodes and edges, together with the network diameter characterized the non-spatial aspect of development. Second, traditional connectivity metrics (alpha, beta, gamma indices) did not yield any changes in time due to their dependence on the average degree, which remained quite constant in infrastructure networks. Third, areas of high BC extended from 1955 to 2012 into a Y-shaped configuration, driven by the development of the main overarching national freeway system. Closeness centrality results show similar patterns. Fourth, the distribution of the 1955 normalized betweenness centrality values transformed into a more heavy-tail distribution in 2012, which implicated that the most critical nodes became even more critical. Future work will enhance this analysis by using more realistic assumptions and incorporating traffic survey data.