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This study analyses the quasi-consensus of second-order leader-following multi-agent systems in four cases: (i) a disconnected undirected graph; (ii) a connected undirected graph; (iii) a digraph with a spanning tree; (iv) a strong connected digraph. We prove that all quasi-consensus are achieved asymptotically in four cases. In other words, all agents follow the virtual leader at the same velocity and keep a distance from the leader. Furthermore, an unified result of the four cases is given. It is notable that the leader plays a key role in the first case and the third case. At last, some examples and simulations are given to verify the above theoretical results.