Centrality and shortest path length measures for the functional analysis of urban drainage networks

Abstract

AbstractThe objective of this research is to evaluate whether complex dynamics of urban drainage networks (UDNs) can be expressed in terms of their structure, i.e. topological characteristics. The present study focuses on the application of topological measures for describing the transport and collection functions of UDNs, using eight subnetworks of the Dresden sewer network as study cases. All UDNs are considered as weighted directed graphs, where edge weights correspond to structural and hydraulic pipe characteristics which affect flow. Transport functions are evaluated in terms of travel time distributions (TTDs), under the hypothesis that frequency distributions of Single Destination Shortest Paths (SDSP) of nodes to the outlet had similar shapes than TTDs. Assessment of this hypothesis is done based on two-sample Kolmogorov-Smirnov tests and comparisons of statistical moments. Collection analysis, i.e. determination of flow paths, is done based on two approaches: (1) using Edge Betweenness Centrality (EBC), and (2) based on the number of SDSP going through an edge connecting a node to the outlet, referred as Paths. Hydrodynamic simulation results are used to validate the outcomes of graph analysis with actual flow behaviors. Results indicate that given an appropriate edge weighting factor, in this case Residence Time, SDSP has the potential to be used as an indicator for flow transport in UDNs. Moreover, both EBC and Paths values were highly correlated to average flows. The first approach, however, proved to be inadequate for estimating flows near the outlet but appropriate for identifying different paths in meshed systems, while the second approach lead to better results in branched networks. Further studies regarding the influence of UDNs layout are needed.