论文标题
Tikhonov正则化在无向图的邻接矩阵中的广义倒数中应用
Application of Tikhonov Regularization in Generalized Inverse of Adjacency Matrix of Undirected Graph
论文作者
论文摘要
在本文中，我们明确发现了无向图的邻接矩阵的摩尔 - 联合概括。我们证明了矩阵$r_λ= [r_ {ij}] $是非词，其中$ r_ {ii} = \ frac {1}λ+°v_i $和$ r_ {ij} = \米中n_g（v_i） $ a^{\ dagger} _g = [s_ {ij}] _ {1 \ leq i，j \ leq n} $其中$ \ displayStyle {s_ {ij} = s_ {ji} = s_ {ji} = \ lim_ \ rangle} $。主要结果的证明是基于Tikhonov正则化。
In this paper, we found the Moore-Penrose generalized inverse of adjacency matrix of an undirected graph, explicitly. We proved that the matrix $R_λ= [r_{ij}]$ is nonsingular where $r_{ii}=\frac{1}λ+ °v_i$ and $r_{ij}=\mid N_G(V_i)\cap N_G(V_j)\mid$ for $i\neq j$, and we proved that $A^{\dagger}_G=[s_{ij}]_{1\leq i, j \leq n}$ where $\displaystyle{s_{ij}=s_{ji}=\lim_{λ\rightarrow +\infty} \langle R^{-1}_λe_j, f_i \rangle }$. The proof of the main result was based on the Tikhonov regularization.
