Population-based optimisers, such as swarm intelligence and evolutionary algorithms, have been widely applied across various optimisation problems due to their flexibility, efficiency, and balance between exploration and exploitation. However, they can be prone to premature stagnation and suboptimal convergence, especially in complex search spaces. Memetic algorithms that combine Particle Swarm Optimization (PSO) with local search operators have been introduced to address these issues. This paper presents a network-based comparative study of memetic operators for swarm optimisers. As a case study, we selected three memetic PSO variants: PSO with Pattern Search, PSO with Hill Climbing, and PSO with Simulated Annealing. We also assessed three communication topologies for PSO (e.g., Global, Local, and Von Neumann). Using Interaction Networks and metrics such as Portrait Divergence and Interaction Diversity, we model and assess these variants’ convergence behaviour, and exploration-exploitation dynamics over time. Results indicate that the influence of the memetic operators and communication topologies affects different aspects of the network, such as connection patterns, the presence of hubs and clusters, and the edges’ weights. Additionally, the network analysis offers valuable insights into the exploration-exploitation balance, convergence speed, and the role of topological structures in shaping swarm dynamics.