The observation that disease associated proteins often interact with each other has fueled the development of network-based approaches to elucidate the molecular mechanisms of human disease. Such approaches build on the assumption that protein interaction networks can be viewed as maps in which diseases can be identified with localized perturbation within a certain neighborhood. The identification of these neighborhoods, or disease modules, is therefore a prerequisite of a detailed investigation of a particular pathophenotype. While numerous heuristic methods exist that successfully pinpoint disease associated modules, the basic underlying connectivity patterns remain largely unexplored. In this work we aim to fill this gap by analyzing the network properties of a comprehensive corpus of 70 complex diseases. We find that disease associated proteins do not reside within locally dense communities and instead identify connectivity significance as the most predictive quantity. This quantity inspires the design of a novel Disease Module Detection (DIAMOnD) algorithm to identify the full disease module around a set of known disease proteins. We study the performance of the algorithm using well-controlled synthetic data and systematically validate the identified neighborhoods for a large corpus of diseases.