Complex network theory (CNT) studies the relevance of elements in networks using centrality metrics. From the CNT standpoint, water distribution networks (WDNs) are infrastructure networks composed by vertices, named nodes, connected to each other by edges, named pipes, that transfer water to customers following a transfer process based on shortest paths. The present paper proposes the domain analysis of several real WDNs using the edge betweenness in order to capture the hydraulic behaviour based on network structure, i.e., for understanding the role of topological features in the emergent hydraulic behaviour. The strategy is obtained by tailoring CNT studies and tools in order to (i) embed the different hydraulic roles of sources and demand nodes, (ii) move the classic concept of centrality from the nodes to the pipes, i.e., the technically relevant components for WDNs and (iii) include information related to the directional devices, because they constrain flow directions. Results show the usefulness of the novel WDN-tailored edge betweenness for the WDN domain analysis. Therefore, the metric can represent a useful tool for supporting WDNs analysis, design and management tasks.