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. (C) 2009 Elsevier Ltd. All rights reserved.