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.

中文翻译：

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通过图的边积对复杂网络中的高阶交互进行建模

许多图形产品已被应用于生成具有在现实世界系统中观察到的惊人特性的复杂网络。在本文中，我们通过迭代使用边缘电晕积提出了一个简单网络的简单生成模型。我们对网络模型的结构特性进行了综合分析，包括度分布、直径、聚类系数以及团大小的分布，得到了这些相关量的显式表达式，这与在不同的真实网络中发现的行为一致。此外，我们获得了归一化拉普拉斯矩阵的所有特征值及其相关多重性的精确表达式，在此基础上，我们推导出了混合时间、平均命中时间和生成树数量的明确公式。因此，与其他图产品生成的先前模型一样，我们的模型也是一个完全可解的模型，其结构特性可以进行解析处理。更有趣的是，我们模型的光谱表达式也是精确确定的，这与以前的模型形成鲜明对比，后者的光谱最多只能递归给出。这一优势使我们的模型成为研究动态过程的良好试验台和理想的基质网络，特别是那些与归一化拉普拉斯矩阵光谱密切相关的过程，以揭示单纯结构对这些过程的影响。这与以前的模型形成鲜明对比，以前的模型最多只能递归地给出光谱。这一优势使我们的模型成为研究动力学过程的良好试验台和理想的基质网络，特别是那些与归一化拉普拉斯矩阵光谱密切相关的过程，以揭示单纯结构对这些过程的影响。这与以前的模型形成鲜明对比，以前的模型最多只能递归地给出光谱。这一优势使我们的模型成为研究动力学过程的良好试验台和理想的基质网络，特别是那些与归一化拉普拉斯矩阵光谱密切相关的过程，以揭示单纯结构对这些过程的影响。