论文标题
光谱分析及其基于加权M-Clique Annex操作的无标度网络的应用
Spectral Analysis and its applications for a class of scale-free network based on the weighted m-clique annex operation
论文作者
论文摘要
网络的光谱是研究网络功能和动态特性的重要工具，图形操作和产品是构建特定局部和全球拓扑结构的有效机制。在这项研究中，定义了一类加权$ m- $集团附件操作$τ_m^r（\ cdot）$由比例因子$ m $和权重因子$ r $控制，构建了具有迭代加权网络模型$ g_t $，带有小世界和无标度属性。特别是，当迭代$ t $倾向于无穷大时，网络具有转限分形属性。然后，通过网络结构的迭代特征，研究了与网络相对应的标准化拉普拉斯矩阵的特征值的迭代关系。因此，进一步给出了网络频谱的某些应用，包括Kenemy常数，乘法kirchhoff指数和加权跨越树的数量。此外，我们还研究了控制网络操作的两个因素对迭代加权网络$ g_t $的结构和功能的影响，以便网络操作可以更好地模拟真实网络并在人工网络领域具有更大的应用潜力。
The spectrum of network is an important tool to study the function and dynamic properties of network, and graph operation and product is an effective mechanism to construct a specific local and global topological structure. In this study, a class of weighted $m-$clique annex operation $τ_m^r(\cdot)$ controlled by scale factor $m$ and weight factor $r$ is defined, through which an iterative weighted network model $G_t$ with small-world and scale-free properties is constructed. In particular, when the number of iterations $t$ tends to infinity, the network has transfinite fractal property. Then, through the iterative features of the network structure, the iterative relationship of the eigenvalues of the normalized Laplacian matrix corresponding to the network is studied. Accordingly, some applications of the spectrum of the network, including the Kenemy constant, Multiplicative Degree-Kirchhoff index and the number of weighted spanning trees, are further given. In addition, we also study the effect of the two factors controlling network operation on the structure and function of the iterative weighted network $G_t$, so that the network operation can better simulate the real network and have more application potential in the field of artificial network.
