  Many graph products have been applied to generate complex networks with
striking properties observed in real-world systems. In this paper, we propose a
simple generative model for simplicial networks by iteratively using edge
corona product. We present a comprehensive analysis of the structural
properties of the network model, including degree distribution, diameter,
clustering coefficient, as well as distribution of clique sizes, obtaining
explicit expressions for these relevant quantities, which agree with the
behaviors found in diverse real networks. Moreover, we obtain exact expressions
for all the eigenvalues and their associated multiplicities of the normalized
Laplacian matrix, based on which we derive explicit formulas for mixing time,
mean hitting time and the number of spanning trees. Thus, as previous models
generated by other graph products, our model is also an exactly solvable one,
whose structural properties can be analytically treated. More interestingly,
the expressions for the spectra of our model are also exactly determined, which
is sharp contrast to previous models whose spectra can only be given
recursively at most. This advantage makes our model a good test-bed and an
ideal substrate network for studying dynamical processes, especially those
closely related to the spectra of normalized Laplacian matrix, in order to
uncover the influences of simplicial structure on these processes.
