Clustering-Based Model Reduction of Laplacian Dynamics With Weakly Connected Topology

This article studies the structure-preserving model
reduction of Laplacian dynamics, which represent weakly connected directed networks with diffusive couplings. The notion of
clusterability is introduced to guarantee a bounded reduction error, and a clustering algorithm is then proposed to partition the
nodes into clusters, such that the nodes in each cluster form a
connected subgraph of the original network. Then, a reduced-order
model, which is established using the generalized balanced form
of the original network, preserves the weakly connection structure
and consensus property. Finally, the effectiveness of the proposed
approach is illustrated by a numerical example