Lithium-ion batteries play an important role in large-scale energy storage systems. However, the power inconsistency of the battery packs restricts the developments of modern technologies in energy storage area. The motivation of the present study is to serve the growing needs of the energy balance for lithium-ion battery packs. The present study proposes a flexible multiphase interleaved converter for the energy equalization of a lithium battery pack with series configuration. Moreover, the graph theory is applied to the analysis of equalization circuits. It is intended to establish a unified standard for the comparison. The parameter of average efficiency is considered as an important indicator to evaluate the performance of the equilibrium system. This mentioned method is verified by constructing a lithium-ion battery pack with the equalization circuit. It is observed that the proposed multiphase interleaved converter has flexible characteristics, while it has low energy loss compared with the conventional methods. The proposed method simplifies the complex equalization circuits into graphs and facilitates the comparison of the average efficiency of the system. It is concluded that this method is a feasible and powerful for evaluating the battery equalization circuit. This approach can be applied for solving complex problems in other engineering applications.