The paper investigates the impact of population structures on the performance of the particle swarm optimization (PSO) algorithm. It explores various population topologies, including random graphs and special sociometric patterns, to determine which structures lead to better performance. The study finds that previous assumptions about the effectiveness of gbest and lbest topologies may not be entirely accurate. The research focuses on undirected, unweighted, and static population topologies. It examines factors such as the number of neighbors (k), clustering (C), and the average shortest distance between nodes. The study uses five standard test functions to evaluate performance, measuring the best result after 1,000 iterations, the number of iterations required to meet a criterion, and whether the criterion was met. Random graphs were generated with varying k and C values, and their performance was compared. The study found that k=5 performed best in terms of standardized performance and required the fewest iterations to meet the criterion. However, k=3 had the highest success rate in meeting the criterion. Special sociometric patterns, such as gbest, lbest, pyramid, star, von Neumann, and small, were also tested. The von Neumann neighborhood performed well, ranking second in performance and third in proportion meeting the criterion. The star configuration, a centralized topology, performed poorly, with a function performance 1.396 standard deviations above the mean. The study concludes that the optimal population structure depends on the dependent measure used. Greater connectivity speeds up convergence but does not necessarily improve the population's ability to find global optima. The von Neumann configuration was recommended as it performed more consistently than commonly used topologies. The research highlights the importance of considering population topology in PSO and suggests that further investigation is needed to identify the best structures for different problems.The paper investigates the impact of population structures on the performance of the particle swarm optimization (PSO) algorithm. It explores various population topologies, including random graphs and special sociometric patterns, to determine which structures lead to better performance. The study finds that previous assumptions about the effectiveness of gbest and lbest topologies may not be entirely accurate. The research focuses on undirected, unweighted, and static population topologies. It examines factors such as the number of neighbors (k), clustering (C), and the average shortest distance between nodes. The study uses five standard test functions to evaluate performance, measuring the best result after 1,000 iterations, the number of iterations required to meet a criterion, and whether the criterion was met. Random graphs were generated with varying k and C values, and their performance was compared. The study found that k=5 performed best in terms of standardized performance and required the fewest iterations to meet the criterion. However, k=3 had the highest success rate in meeting the criterion. Special sociometric patterns, such as gbest, lbest, pyramid, star, von Neumann, and small, were also tested. The von Neumann neighborhood performed well, ranking second in performance and third in proportion meeting the criterion. The star configuration, a centralized topology, performed poorly, with a function performance 1.396 standard deviations above the mean. The study concludes that the optimal population structure depends on the dependent measure used. Greater connectivity speeds up convergence but does not necessarily improve the population's ability to find global optima. The von Neumann configuration was recommended as it performed more consistently than commonly used topologies. The research highlights the importance of considering population topology in PSO and suggests that further investigation is needed to identify the best structures for different problems.