Understanding the factors that affect the occurrence of failures in urban drainage networks (UDNs) is a key concept for developing strategies to improve the reliability of such systems. Although a lot of research has been done in this field, the relationship between UDN structure (i.e. layout) and its functional failures is still unclear. In this context, the present study focuses first on determining which are the most common sewer layout topologies, based on a data set of 118 UDNs, and then on analyzing the relationship between these and the occurrence of node flooding using eight subnetworks of the sewer system of Dresden, Germany, as a study case. A method to 'quantify' the topology of a UDN in terms of similarity to a branched or meshed system, referred to as Meshness, is introduced. Results indicate, on the one hand, that most networks have branched or predominantly branched topologies. On the other hand, node flooding events in networks with higher Meshness values are less likely to occur, and have shorter durations and smaller volumes than in predominantly branched systems. Predominantly meshed systems are identified then as more reliable in terms of flooded nodes and flooding volumes.