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In this paper, we establish a method for model order reduction of a certainclass of physical network systems. The proposed method is based on clusteringof the vertices of the underlying graph, and yields a reduced order modelwithin the same class. To capture the physical properties of the network, weallow for weights associated to both the edges as well as the vertices of thegraph. We extend the notion of almost equitable partitions to this class ofgraphs. Consequently, an explicit model reduction error expression in the senseof H2-norm is provided for clustering arising from almost equitable partitions.Finally the method is extended to second-order systems.

Structure-preserving model reduction of physical network systems by clustering