In this paper, we investigate the historical development of complex network topologies in urban water distribution networks (WDNs) and urban drainage networks (UDNs). The analyses were performed on time-stamped network data of an Alpine case study, which represent the evolution of the town and its infrastructure over the past 106 years. We use the dual representation of the network, where pipes are considered as nodes and intersections as edges, respectively. The functional topologies of the networks are analyzed based on the dual graph, providing insights beyond a conventional graph (primal mapping) analysis. We observe that the WDNs and UDNs show scale-free network characteristics and evolve with consistent patterns over time. However, structural differences between both network types are found in the node degree distributions and the characteristic path lengths, resulting from different functionalities of the systems. Finally, we show the remapping of the dual network characteristics to the spatial map and discuss possibilities for further applications.