Its focus on dependencies and patterns in relational data makes network science a promising addition to the analytic toolbox in archaeology. Despite its tradition in a number of other fields, however, the methodology of network science is only in development and its scope and proper usage are subject to debate. We argue that the historical linkage with graph theory and limitations in commonly available software form an obstacle to leveraging the full potential of network methods. This is illustrated via replication of a study of Maya obsidian (Golitko et al. Antiquity, 2012), in which it seemed necessary to discard detailed information in order to represent data in networks suitable for further processing. We propose means to avoid such information loss by using methods capable of handling valued rather than binarized data. The resulting representations corroborate previous conclusions but are more reliable and thus justify a more detailed interpretation of shifting supply routes as an underlying process contributing to the collapse of Maya urban centers. Some general conclusions for the use of network science in archaeology are offered. © 2016 Published by Elsevier Ltd.