In this paper, we propose a clustered model reduction method for interconnected second-order systems evolving over undirected networks, which we call second-order networks. In this model reduction method, network clustering, i.e., clustering of subsystems, is performed according to cluster reducibility, which is defined as a notion of weak controllability of local subsystem states. This paper clarifies that the cluster reducibility can be algebraically characterized for second-order networks through the controller-Hessenberg transformation of their first-order representation. By aggregating the reducible clusters, we obtain an approximate model that preserves an interconnection topology among clustered subsystems. Furthermore, we derive an H_∞-error bound of the state discrepancy caused by the cluster aggregation. Finally, the efficiency of the proposed method is demonstrated through an example of large-scale complex networks.