The formation of HBr has long been widely regarded as proceeding via a chain-reaction pathway comprising the initiation step, activated catalytically, thermally, electrically, photonically or collisionally, the propagation steps, and termination step. In recent years, however, it has been recognized that this chain-reaction pathway or mechanism does not give rise to stoichiometrically closure, thereby violating the axiomatic laws of mass conservation and stoichiometric constraint of chemical reactions. Proposed herein is a novel chain-reaction mechanism involving the activation of hydrogen in addition to that of bromine to initiate the chain. By resorting to the mathematically rigorous, graph-theoretic algorithmic method based on a unique bipartite graph, P-graph (process graph), two stoichiometrically feasible independent pathways and one acyclic combined pathway have been obtained from this novel chain-reaction mechanism. The algorithmic method deployed is based on the two sets of axioms, one being the set of 6 axioms of feasible reaction pathways and the other being the set of 7 axioms of combinatorially feasible networks, and graph representation of reaction steps in terms of P-graphs.