We propose a structure-preserving model-reduction methodology for large-scale dynamic networks with tightly-connected components. First, the coherent groups are identified by a spectral clustering algorithm on the graph Laplacian matrix that models the network feedback. Then, a reduced network is built, where each node represents the aggregate dynamics of each coherent group, and the reduced network captures the dynamic coupling between the groups. We provide an upper bound on the approximation error when the network graph is randomly generated from a weight stochastic block model. Finally, numerical experiments align with and validate our theoretical findings.

翻译：我们提出一种面向大规模动态网络的结构保持模型降阶方法，该方法适用于包含紧连接组件的网络系统。首先，通过在图拉普拉斯矩阵（该矩阵建模网络反馈）上应用谱聚类算法识别相干群组；然后构建一个降阶网络，其中每个节点代表对应相干群组的聚合动态特性，且该降阶网络能够捕捉群组间的动态耦合。针对网络图由权重随机块模型随机生成的情形，我们给出了近似误差的上界。最后，数值实验验证了我们的理论结果。