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