In this study, we propose a new graph-theoretical method to simulate guidewire paths inside the carotid artery. The minimum energy guidewire path can be obtained by applying the shortest path algorithm, such as Dijkstra's algorithm for graphs, based on the principle of the minimal total energy. Compared to previous results, experiments of three phantoms were validated, revealing that the first and second phantoms overlap completely between simulated and real guidewires. In addition, 95 % of the third phantom overlaps completely, and the remaining 5 % closely coincides. The results demonstrate that our method achieves 87 and 80 % improvements for the first and third phantoms under the same conditions, respectively. Furthermore, 91 % improvements were obtained for the second phantom under the condition with reduced graph construction complexity.