A systematic approach was developed to obtain analytic solutions for the concentrations of the quasi steady state (QSS) species in reduced mechanisms. The nonlinear algebraic equations for the QSS species concentrations were first approximated by a set of linear equations, and the linearized quasi steady state approximations (LQSSA) were then analytically solved with a directed graph, namely a QSSG, which was abstracted from the inter-dependence of QSS species. To obtain analytic solutions of high computational efficiency, the groups of strongly connected QSS species were first identified in the QSSG. The inter group couplings were then resolved by a topological sort, and the inner group couplings were solved with variable elimination by substitution. An efficient algorithm was developed to identify a near-optimal sequence for the variable elimination process. The proposed LQSSA-QSSG method was applied to generate a 16-step reduced mechanism for ethylene/air, and good accuracy and high efficiency were observed in simulations of autoignition and perfectly stirred reactors with the reduced mechanism.