Water distribution networks are infrastructural systems designed for providing potable water to consumers. In these last decades, the importance of assessing and identifying emerging leakages has become a primary issue, because of the high level of water loss characterizing such systems worldwide. In this paper, a new approach aimed at the prompt localization of leakages occurring in water distribution systems is introduced. The methodology relies on the analysis of real-time pressure measurements and on Complex Networks Theory. Starting from a collection of nodes representing the locations of pressure sensors, links of a virtual, complex network are created on the basis of the values assumed by correlation coefficients between pressure measurements: if such values are above a given threshold, relevant nodes are considered to be connected to each other. In this way, information about the structure and topology of the complex network is easily derived. In particular, the degree centrality of the nodes is a key parameter allowing to identify the position of a leakage. The paper first analyzes a well-known literature example, and then proves the high reliability of the methodology for a real water distribution system.