  While renormalization groups are fundamental in physics, renormalization of
complex networks remains vague in its conceptual definition and methodology.
Here, we propose a novel strategy to renormalize complex networks. Rather than
resorting to handling the bare structure of a network, we overlay it with a
readily renormalizable physical model, which reflects real-world scenarios with
a broad generality. From the renormalization of the overlying system, we
extract a rigorous and simple renormalization group transformation of arbitrary
networks. In this way, we obtain a transparent, model-dependent physical
meaning of the network renormalization, which in our case is a scale
transformation preserving the transition dynamics of low-density particles. We
define the strength of a node in accordance with the physical model and trace
the change of its distribution under our renormalization process. This analysis
demonstrates that the strength distributions of scale-free networks remain
scale-invariant, whereas those of homogeneous random networks do not.
