This paper concentrates on the design of an event-triggered communication strategy for secondary multi-agent systems. Many existing results in this field usually require centralized information depending on the Laplacian matrices. In a real application, however, such the constraint is conservative. To address it, this paper proposes an event-triggered sampling mechanism for interagent communication with updated thresholds. Accordingly, consensus protocols with adaptive coupling control gains are proposed for both a fixed topology and switching topologies. It is proven that the proposed method guarantees the leader-following consensus for second-order multiagent systems with an arbitrarily connected topology and even with jointly connected switching topologies. The effectiveness of the proposed scheme is verified by simulation examples.