论文标题
Chung-lu随机图的主要特征值和特征向量的中央限制定理
Central limit theorem for the principal eigenvalue and eigenvector of Chung-Lu random graphs
论文作者
论文摘要
Chung-lu随机图是一个不均匀的Erdős-rényi随机图，其中为平均度分配了顶点，并且对顶点对与平均度度成正比的边缘连接，而不同边缘则独立于其平均度。我们得出了主要特征值的中心限制定理和chung-lu随机图的邻接矩阵的主要特征向量的组成部分。我们的派生需要在平均程度上进行某些假设，以确保图形的连通性，稀疏性和有限的不均匀性。
A Chung-Lu random graph is an inhomogeneous Erdős-Rényi random graph in which vertices are assigned average degrees, and pairs of vertices are connected by an edge with a probability that is proportional to the product of their average degrees, independently for different edges. We derive a central limit theorem for the principal eigenvalue and the components of the principal eigenvector of the adjacency matrix of a Chung-Lu random graph. Our derivation requires certain assumptions on the average degrees that guarantee connectivity, sparsity and bounded inhomogeneity of the graph.
