A note on connectivity of multi-agent systems with proximity graphs and linear feedback protocol

In this note, we investigate the possibility of simplifying the connectivity verification for multi-agent systems with proximity graphs and the linear feedback protocol. A Lyapunov-like approach is developed for analyzing the monotonicity of the largest edge length in the network. Based on this approach, we provide an initial-connectivity-based sufficient condition for dynamic connectivity. In particular, when each initial node degree is not less than three fourth of the graph order, initial network connectivity implies dynamic connectivity.