Abstract: To intuitively grasp the network distribution and path tracing of carbon emission flows from the generation side to the load side through the network in the power system and to improve the physical process of carbon emission accounting and responsibility sharing, the paper proposes a graph theory-based carbon flow analysis method. Firstly, the network distribution and path-tracing process of carbon emission flow is deduced and analyzed in a simple system. Then, the deduction process is broadened to the general power system. The carbon flow network distribution algorithm based on breadth-first search is put forward, which achieves the layer-by-layer distribution calculation of the system's carbon emission flow. Then, a carbon flow path tracking algorithm based on depth-first search is proposed to track the feasible path from the power generation side to the load side and the carbon flow contribution along the path in the lossy network system. Combined with the carbon flow path decomposition algorithm, the carbon flow along the path is obtained. Finally, the algorithm's effectiveness is verified in the IEEE14-node system by comparing it with the results of matrix calculation and further verified in the complex network IEEE118-node system. The carbon flow analysis method based on graph theory improves the shortcomings of existing methods in carbon flow network distribution and path tracing, and has certain practical value and reference significance.