We present a method that enables resilient formation control for mobile robot teams in the presence of noncooperative (defective or malicious) robots. Recent results in network science define graph topological properties that guarantee resilience against faults and attacks on individual nodes in static networks. We build on these results to propose a control policy that allows a team of mobile robots to achieve resilient consensus on the direction of motion. Our strategy relies on dynamic connectivity management that makes use of a metric that characterizes the robustness of the communication network topology. Our method distinguishes itself from prior work in that our connectivity management strategy ensures that the network lies above a critical resilience threshold, guaranteeing that the consensus algorithm always converges to a value within the range of the cooperative agents’ initial values. We demonstrate the use of our framework for resilient flocking, and show simulation results with groups of holonomic mobile robots.