Owing to emergence of density functional theory (DFT) and dramatic enhancement of computer performance, computational chemistry has become a useful tool for mechanism study of chemical reactions. However, prediction of reaction paths is still challenging due to high complexity of chemical space and high computational costs. Roles of computational chemistry have usually been limited to verifying the suggested mechanisms, which can lead to biased results. To overcome these limitations, development of an efficient and reliable method is necessary. Here, we develop the program for automated prediction of reaction mechanism based on graph theory. It focuses on optimal collaboration of chemical heuristic rules, graph-theoretic analysis and first-principle calculations. Our program consists of several steps; as the first step, possible intermediate states for a given reaction are sampled by either stochastic sampling or combinatorial enumeration of molecular graphs. Then, the reaction network is constructed. Intermediates are connected as edges or elementary reaction steps. The distance of an edge is related to activation energy of the reaction. A significant feature of our program is to evaluate activation energy rapidly through analysis of molecular graphs of intermediates. Estimation of activation energy does not rely on any conventional methods or quantum-chemical calculations for finding transition states. As the final step, a kinetic analysis is performed to extract a minimal subnetwork and determine kinetically favorable reaction mechanisms. This result can be further verified by investigation of energetics using conventional quantum-chemical calculations. Our program was successful to find reliable mechanisms for several reaction examples with less computational costs.