Network science provides a rich set of theories and methods to understand the structure and dynamics of complex social, information, and biological systems. These approaches traditionally demand data with explicitly declared dyadic relationships or interactions such as friendship or affiliation. However, socio-technical systems like Wikipedia, Github, or Twitter often encode latent relationships within event logs and other databases. Using several case studies, I describe how complex networks called 'socio-technical trajectories' can be extracted from event logs to understand the behavior of both users and artifacts within these systems. These trajectories encode a variety of rich structural and dynamic data distinct from traditional network approaches and illustrate user social roles within distributed collaboration as well as context and shifting interests of users based on their contributions. This approach has rich implications for mixed-methods research as it allows researchers to collapse large-scale event log data into more parsimonious network representations that can motivate qualitative analysis, visualization, and statistical modeling of complex user behavior.