  Various graph products and operations have been widely used to construct
complex networks with common properties of real-life systems. However, current
works mainly focus on designing models of binary networks, in spite of the fact
that many real networks can be better mimicked by heterogeneous weighted
networks. In this paper, we develop a corona product of two weighted graphs,
based on which and an observed updating mechanism of edge weight in real
networks, we propose a minimal generative model for inhomogeneous weighted
networks. We derive analytically relevant properties of the weighted network
model, including strength, weight and degree distributions, clustering
coefficient, degree correlations and diameter. These properties are in good
agreement with those observed in diverse real-world weighted networks. We then
determine all the eigenvalues and their corresponding multiplicities of the
transition probability matrix for random walks on the weighted networks.
Finally, we apply the obtained spectra to derive explicit expressions for mean
hitting time of random walks and weighted counting of spanning trees on the
weighted networks. Our model is an exactly solvable one, allowing to
analytically treat its structural and dynamical properties, which is thus a
good test-bed and an ideal substrate network for studying different dynamical
processes, in order to explore the impacts of heterogeneous weight distribution
on these processes.
