The weighted self-similar network is introduced in an iterative way. In order to understand the topological properties of the self-similar network, we have done a lot of research in this field. Firstly, according to the symmetry feature of the self-similar network, we deduce the recursive relationship of its eigenvalues at two successive generations of the transition-weighted matrix. Then, we obtain eigenvalues of the Laplacian matrix from these two successive generations. Finally, we calculate an accurate expression for the eigentime identity and Kirchhoff index from the spectrum of the Laplacian matrix.

中文翻译：

---

置换规则在马尔可夫谱在加权分区网络中的应用

加权自相似网络以迭代方式引入。为了了解自相似网络的拓扑特性，我们在该领域进行了大量研究。首先，根据自相似网络的对称性，推导了其在过渡加权矩阵的两个连续世代中其特征值的递归关系。然后，我们从这两个连续的世代中获得拉普拉斯矩阵的特征值。最后，我们从拉普拉斯矩阵的光谱中计算出本征时间恒等式和基尔霍夫指数的精确表达式。