As originally shown by King and Altman, graph theory, and specifically the use of spanning trees, provides the means to solve the kinetics of any catalytic network in a steady state regime, taking as input data all the rate constants. Herein, it is shown that the translation of the rate constants to Gibbs energies provides a simpler way to estimate the energy span (i.e., the apparent activation energy of the full reaction), the determining states, and the turnover frequency (TOF) of any and all catalytic networks. By re-examining the concepts of chemical kinetics through rigorous mathematical treatment, an alternative definition is suggested for the term "chemical mechanism". In addition, and in analogy to electrical circuits, the chemical resistor terms (called here "kinestors") are identified for parallel and series chemical circuits, providing a new Ohmic interpretation for catalysis.