A Century of Topological Coevolution of Complex Infrastructure Networks in an Alpine City

Abstract

In this paper, we used complex network analysis approaches to investigate topological coevolution over a century for three different urban infrastructure networks. We applied network analyses to a unique time-stamped network data set of an Alpine case study, representing the historical development of the town and its infrastructure over the past 108 years. The analyzed infrastructure includes the water distribution network (WDN), the urban drainage network (UDN), and the road network (RN). We use the dual representation of the network by using the Hierarchical Intersection Continuity Negotiation (HICN) approach, with pipes or roads as nodes and their intersections as edges. The functional topologies of the networks are analyzed based on the dual graphs, providing insights beyond a conventional graph (primal mapping) analysis. We observe that the RN, WDN, and UDN all exhibit heavy tailed node degree distributions $[P(k)]$ with high dispersion around the mean. In 50 percent of the investigated networks, $P(k)$ can be approximated with truncated [Pareto] power-law functions, as they are known for scale-free networks. Structural differences between the three evolving network types resulting from different functionalities and system states are reflected in the $P(k)$ and other complex network metrics. Small-world tendencies are identified by comparing the networks with their random and regular lattice network equivalents. Furthermore, we show the remapping of the dual network characteristics to the spatial map and the identification of criticalities among different network types through co-location analysis and discuss possibilities for further applications.