This paper presents a graph-based approach for optimizing the positions of movable antennas (MAs) in a multiple-input single-output (MISO) communication system to maximize received signal power. Unlike previous methods that search for optimal positions continuously, the authors discretize the transmit region into sampling points and model the problem as a shortest path problem in graph theory. This allows for an optimal solution in polynomial time using a customized algorithm, and a suboptimal solution in linear time using a sequential update algorithm. Numerical results show that the proposed algorithms significantly outperform conventional fixed-position antennas (FPAs) with and without antenna selection. The system model involves a MISO setup with multiple MAs at the transmitter and a single fixed-position antenna (FPA) at the receiver. The MAs can be positioned at discrete sampling points along a linear array, with a minimum distance constraint to avoid mutual coupling. The goal is to select sampling points for the MAs to maximize the received signal power, which is determined by the sum of the squared magnitudes of the channel responses at the selected points. The problem is formulated as an optimization problem (P1) where the objective is to maximize the sum of the squared magnitudes of the channel responses at the selected sampling points, subject to constraints on the minimum distance between MAs. The authors show that this problem can be transformed into a shortest path problem in a graph, where the vertices represent sampling points and the edges represent the channel responses. The optimal solution is found by solving this shortest path problem, while the suboptimal solution is obtained through a sequential update algorithm that iteratively selects the best sampling points for the MAs. Numerical results demonstrate that the proposed algorithms achieve significant performance gains over conventional FPAs, with the optimal algorithm outperforming the suboptimal one. The results also show that the performance of the proposed algorithms improves with the number of sampling points and the number of MAs, but the gains diminish as the number of MAs increases due to the distance constraints. The sequential update algorithm achieves near-optimal performance but may fail to find the optimal positions in some cases. The results highlight the effectiveness of the graph-based approach in optimizing MA positions for improved communication performance.This paper presents a graph-based approach for optimizing the positions of movable antennas (MAs) in a multiple-input single-output (MISO) communication system to maximize received signal power. Unlike previous methods that search for optimal positions continuously, the authors discretize the transmit region into sampling points and model the problem as a shortest path problem in graph theory. This allows for an optimal solution in polynomial time using a customized algorithm, and a suboptimal solution in linear time using a sequential update algorithm. Numerical results show that the proposed algorithms significantly outperform conventional fixed-position antennas (FPAs) with and without antenna selection. The system model involves a MISO setup with multiple MAs at the transmitter and a single fixed-position antenna (FPA) at the receiver. The MAs can be positioned at discrete sampling points along a linear array, with a minimum distance constraint to avoid mutual coupling. The goal is to select sampling points for the MAs to maximize the received signal power, which is determined by the sum of the squared magnitudes of the channel responses at the selected points. The problem is formulated as an optimization problem (P1) where the objective is to maximize the sum of the squared magnitudes of the channel responses at the selected sampling points, subject to constraints on the minimum distance between MAs. The authors show that this problem can be transformed into a shortest path problem in a graph, where the vertices represent sampling points and the edges represent the channel responses. The optimal solution is found by solving this shortest path problem, while the suboptimal solution is obtained through a sequential update algorithm that iteratively selects the best sampling points for the MAs. Numerical results demonstrate that the proposed algorithms achieve significant performance gains over conventional FPAs, with the optimal algorithm outperforming the suboptimal one. The results also show that the performance of the proposed algorithms improves with the number of sampling points and the number of MAs, but the gains diminish as the number of MAs increases due to the distance constraints. The sequential update algorithm achieves near-optimal performance but may fail to find the optimal positions in some cases. The results highlight the effectiveness of the graph-based approach in optimizing MA positions for improved communication performance.