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Many graph products have been applied to generate complex networks withstriking properties observed in real-world systems. In this paper, we propose asimple generative model for simplicial networks by iteratively using edgecorona product. We present a comprehensive analysis of the structuralproperties of the network model, including degree distribution, diameter,clustering coefficient, as well as distribution of clique sizes, obtainingexplicit expressions for these relevant quantities, which agree with thebehaviors found in diverse real networks. Moreover, we obtain exact expressionsfor all the eigenvalues and their associated multiplicities of the normalizedLaplacian matrix, based on which we derive explicit formulas for mixing time,mean hitting time and the number of spanning trees. Thus, as previous modelsgenerated 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, whichis sharp contrast to previous models whose spectra can only be givenrecursively at most. This advantage makes our model a good test-bed and anideal substrate network for studying dynamical processes, especially thoseclosely related to the spectra of normalized Laplacian matrix, in order touncover the influences of simplicial structure on these processes.

Edge corona product as an approach to modeling complex simplical networks