Data from online social networks carry enormous potential for psychological research, yet their use and the ethical implications thereof are currently hotly debated. The present work aims to outline in detail the unique information richness of this data type and, in doing so, to support researchers when deciding on ethically appropriate ways of collecting, storing, publishing, and sharing data from online sources. Focusing on the very nature of social networks, their structural characteristics, and depth of information, we provide a detailed and accessible account of the challenges associated with data management and data storage. In particular, the general nonanonymity of network data sets is discussed, and an approach is developed to quantify the level of uniqueness that a particular online network bestows upon the individual maintaining it. Using graph enumeration techniques, we show that comparatively sparse information on a network is suitable as a sociometric marker that allows for the identification of an individual from the global population of online users. The impossibility of anonymizing specific types of network data carries implications for ethical guidelines and research practice. At the same time, network uniqueness opens up opportunities for novel research in psychology.