The paper explores the impact of population structure on the performance of the particle swarm optimization (PSO) algorithm. The authors analyze the trajectories of individual particles in a PSO population and highlight the importance of dynamic interactions among particles. They compare two common population structures: gbest, where each particle's trajectory is influenced by the best point found by any member of the entire population, and lbest, where each particle is influenced by a smaller number of adjacent members. The study focuses on undirected, unweighted, and non-changing connections within the population. Key factors affecting performance include the degree of connectivity ($k$), clustering ($C$), and the average shortest distance between nodes. The authors hypothesize that heterogeneous population structures, with some subsets tightly connected and others isolated, might combine the benefits of both gbest and lbest sociometries. Five standard test functions (Sphere, Rastrigin, Griewank, Rosenbrock, and Shaffer's f6) are used to evaluate the performance of different population topologies. The dependent variables include the best function result after 1,000 iterations, the proportion of trials meeting a criterion, and the median number of iterations required to meet the criterion. The research uses random graphs and special graphs designed by the researchers to test various population structures. The results show that higher connectivity ($k=5$) generally leads to better performance, with the von Neumann neighborhood and the pyramid sociometry performing particularly well. The star configuration, a centralized topology, performs poorly. The study concludes that the von Neumann configuration, which has moderate connectivity, is recommended for future PSO research due to its consistent performance across different functions.The paper explores the impact of population structure on the performance of the particle swarm optimization (PSO) algorithm. The authors analyze the trajectories of individual particles in a PSO population and highlight the importance of dynamic interactions among particles. They compare two common population structures: gbest, where each particle's trajectory is influenced by the best point found by any member of the entire population, and lbest, where each particle is influenced by a smaller number of adjacent members. The study focuses on undirected, unweighted, and non-changing connections within the population. Key factors affecting performance include the degree of connectivity ($k$), clustering ($C$), and the average shortest distance between nodes. The authors hypothesize that heterogeneous population structures, with some subsets tightly connected and others isolated, might combine the benefits of both gbest and lbest sociometries. Five standard test functions (Sphere, Rastrigin, Griewank, Rosenbrock, and Shaffer's f6) are used to evaluate the performance of different population topologies. The dependent variables include the best function result after 1,000 iterations, the proportion of trials meeting a criterion, and the median number of iterations required to meet the criterion. The research uses random graphs and special graphs designed by the researchers to test various population structures. The results show that higher connectivity ($k=5$) generally leads to better performance, with the von Neumann neighborhood and the pyramid sociometry performing particularly well. The star configuration, a centralized topology, performs poorly. The study concludes that the von Neumann configuration, which has moderate connectivity, is recommended for future PSO research due to its consistent performance across different functions.