On Mesh Currents and Kirchhoff's Current Models

ABSTRACT A new approach to mesh currents is presented, shedding light on their hitherto rather elusive nature. It stems from a reformulation of Kirchhoff's current model, based on the introduction of several new concepts about graphs (namely, flows, cutting flows, subflows, flow partitions, flow equivalence, swirls). Simply put, it is shown that mesh currents are a special case of the so‐called swirl currents, which are defined for both planar and non‐planar biconnected circuits. An illustrative example is also developed in detail: the determination of a current basis consisting of swirl currents for the complete bipartite graph of order (3, 3).