This paper proposes a topology derivation method based on graph theory, which can obtain topologies that meet specified power requirements given the port type, the number of components, and the target function of the circuit. The method uses graph theory to represent the circuit topology with an adjacency matrix. All closed loops can be obtained using a breadth/depth-first search method. Following this, initial topologies that match the required type and number of devices can be found. Circuit rules and the target circuit function can be converted into matrix constraints. Matrices that violate the constraints are then deleted to remove undesired topologies. A transformerless inverter without leakage current is explored as an example of the target function. The method yields several basic topologies with the minimum number of switches that meet the requirements. Expanding on this, working mode analysis and simulation of an integrated boost inverter are carried out to verify the validity of the method and the inverter topology result.