Electric circuits and river networks share similarities in both their network structure and derivation from conservation principals. However, the disciplines have evolved separately and developed methods and models. This paper presents the foundations for network analysis for both disciplines and shows how numerical methods developed for circuit simulations can significantly improve river network models. The equations, models, and jargon are described, providing a reference for future studies to transfer knowledge across disciplinary boundaries. © 2014 B. R. Hodges and F. Liu.