This paper presents a comprehensive study on the impact of information flow topologies on the resilience of distributed algorithms that are widely used for estimation and control in vehicle platoons. In the state of the art, the influence of information flow topology on both internal and string stability of vehicle platoons has been well studied. However, understanding the impact of information flow topology on cyber-security tasks, e.g., attack detection, resilient estimation and formation algorithms, is largely open. By means of a general graph theory framework, we study connectivity measures of several platoon topologies and we reveal how these measures affect the ability of distributed algorithms to reject communication disturbances, to detect cyber-attacks, and to be resilient against them. We show that the traditional platoon topologies relying on interaction with the nearest neighbor are very fragile with respect to performance and security criteria. On the other hand, appropriate platoon topologies, namely k-nearest neighbor topologies, are shown to fulfill desired security and performance levels. The framework we study covers undirected and directed topologies, ungrounded and grounded topologies, or topologies on a line and on a ring. We show that there is a trade-off in the network design between the robustness to disturbances and the resilience to adversarial actions. Theoretical results are validated via simulations.