Lateral flow tests (LFTs) are well-suited for rapid point-of-care testing in low resource settings. The wicking action of the paper strip moves the sample and reagents through the device without a need for pumps, but LFTs are typically limited to tests that can be carried out in a single fluidic step. The materials from LFTs can be reconfigured to create paper networks that automatically carry out multi-step fluidic operations, while retaining the same easy-to-use format as a conventional LFT. Here, we describe basic principles of wicking and system-level behavior of paper networks by analogy to electrical circuits. We describe key design principles for a previously-developed 2D paper network (2DPN) and introduce an alternative linear paper network (Pseudo-1DPN) that takes advantage of system-level behavior to perform clean sequential fluid delivery while reducing device running time.