Google矩阵和它的性质

网页等级(PageRank)是一个反映网页重要性的数值.当一个网页A连向另一个网页B的时候,A就等于给网页B投了有效的一票.一个网页接受的票越多,这个网页就越重要.同时,给网页B投票的网页本身的等级也决定了该选票的重要性.Google通过每张选票本身重要性和得票多少来计算一个网页的级别(重要性).Google的核心就是计算每一个网页的等级(即PageRank).本文主要介绍Google矩阵的定义和产生,解释PageRank的一些相关概念,证明Google矩阵及其第二特征值具有的一些性质,并简要介绍这些性质的应用.

Google Matrix and Its Characterizations

PageRank is a numeric value that represents how important a page is on the web.When one page links to another one,it effectively casts a vote for the page.The more votes cast for a page,the more important the page is considered to be.Also the importance of the page that is casting the vote determines how important the vote itself is.The core of Google is to calculate a web page's importance from the votes cast for it while the importance of each vote is taken into accounts.In this paper we first introduce the basic definition of Google matrix and its origination,then explain some relevant terminology.Also presented are some features of Google matrices.We end up the paper with a brief introduction to applications of these features.