The swarm-based P2P networks research area evolved to a mature state due to studies related to algorithms for efficient data exchange. However, comparatively less attention has been given to the overlay network topological characteristics, which result from connections between peers. In swarm-based networks, there are three known connection management strategies: inactive, preemptive and pro-active. So far, there has been no previous work comparing these three strategies under the same scenarios. This paper presents a model based on evolving graphs to describe the resulting system topology according to network configuration and connection management strategies. Base on this model, we analyze the robustness and performance potential of topologies under different peer arrival patterns and network reachability ratios in two distinct moments: at the end of the arrival period and in the steady-state period. Our findings show that, in all scenarios, the preemptive and pro-active strategies generate topologies with higher robustness, because they distribute more uniformly connections among all peers, and better performance due to greater centralization of the content source in the overlay topology.