The information gained when practicing curiosity promotes well-being over extended timescales. The open-ended and internally driven nature of curiosity, however, makes characterizing the diverse styles of information seeking that accompany it a daunting endeavor. A recently developed historicophilosophical taxonomy of curious practice distinguishes between the collection of disparate, loosely connected pieces of information and the seeking of related, tightly connected pieces of information. With this taxonomy, we use a novel knowledge network building framework of curiosity to capture styles of curious information seeking in 149 participants as they explore Wikipedia for over 5 hours spanning 21 days. We create knowledge networks in which nodes consist of distinct concepts (unique Wikipedia pages) and edges represent the similarity between the content of Wikipedia pages. We quantify the tightness of each participants' knowledge networks using graph theoretical indices and use a generative model of network growth to explore mechanisms underlying the observed information seeking. We find that participants create knowledge networks with small-world and modular structure. Deprivation sensitivity, the tendency to seek information that eliminates knowledge gaps, is associated with the creation of relatively tight networks and a relatively greater tendency to return to previously-visited concepts. We further show that there is substantial within-person variability in knowledge network building over time and that building looser networks than usual is linked with higher than usual sensation seeking. With this framework in hand, future research can quantify the information collected during curious practice and examine its association with well-being.