Based on the master equation with the inherent structure of conformation network, the authors investigate some important issues in the folding kinetics of lattice polymers. First, the topologies of conformation networks are discussed. Moreover, a new scheme of implementing Metropolis algorithm, which fulfills the condition of detailed balance, is proposed. Then, upon incorporating this new scheme into the geometric structure of conformation network the authors provide a theorem which can be used to place an upper bound on relaxation time. To effectively identify the kinetic traps of folding, the authors also introduce a new quantity, which is employed from the continuous time Monte Carlo method, called rigidity factor. Throughout the discussions, the authors analyze the results for different move sets to demonstrate the methods and to study the features of the kinetics of folding.