论文标题
瓦特·史特罗加茨随机图的特征值分布
The Eigenvalue Distribution of the Watt-Strogatz Random Graph
论文作者
论文摘要
本文研究了瓦茨 - strogatz随机图的特征值分布，该图被称为“小世界”随机图。小世界随机图的构造始于n个顶点的常规环晶格。每个侧面都有恰好的K邻居。使用概率p，特定顶点的每个下行邻居将独立地重新布线为图上的随机顶点，而无需进行自动环或重复。重新布线的过程始于顶点1的第一个相邻邻居，并以有序的方式延伸至顶点n的最远旁边邻居。必须考虑每个边缘一次。本文重点介绍用于表示小世界随机图的邻接矩阵A_N的特征值。我们计算了第一刻，第二时刻，并证明了限制的第三刻，因为n进入了特征值分布的无穷大。
This paper studies the eigenvalue distribution of the Watts-Strogatz random graph, which is known as the "small-world" random graph. The construction of the small-world random graph starts with a regular ring lattice of n vertices; each has exactly k neighbors with equally k/2 edges on each side. With probability p, each downside neighbor of a particular vertex will rewire independently to a random vertex on the graph without allowing for self-loops or duplication. The rewiring process starts at the first adjacent neighbor of vertex 1 and continues in an orderly fashion to the farthest downside neighbor of vertex n. Each edge must be considered once. This paper focuses on the eigenvalues of the adjacency matrix A_n, used to represent the small-world random graph. We compute the first moment, second moment, and prove the limiting third moment as n goes to infinity of the eigenvalue distribution.
