## Problem statement: Analyzing author relationships (2)

I would like to suggest we start with a simpler problem. Let's forget about the contents of a book and how much it influences others. Our model only concerns the existence of an influence.

Fortunately, there is a mathematical method based on the existence of a relationship, called graph theory.  One of the tools used by graph theory is linear algebra. Graph theory has been widely used for a long time.  When the World Wide Web era came, this method was also applied to the principles of web search to implement a basic idea.  If you can find the most influential web page, you should list these results on top of the search results. There is also a lot of research to find a method to automatically compute the influence between web pages.

Probably the most frequently used method for such a web page ranking only considers the linking relationship between web pages. Since this method only uses link information, it doesn't need to know the contents of individual web pages. This method was a breakthrough in web search engine technology. The inventors of this method started a company called Google, using a computed influence rank for listing the search results[bib:pagerank]. Because the method doesn't need to understand the contents of a web page to evaluate that page's ranking, it can used for web pages in any language with any type of content. Furthermore, the ranking can be fully automated. The search engines of some other companies evaluated the rank by hand, but these companies were easily outperformed by Google. Ranking by hand may be more accurate than automated methods but the automated method is much better at updating speed and handling large numbers of web pages.

The method used for web page ranking by Google is called PageRank [bib:pagerank], though this method is based on the traditional technique of eigenanalysis in linear algebra.

In this article, I first provide an overview of graph theory.  I then apply eigenanalysis to rank the influence of authors.

Therefore, my next blog entry will be ``introduction to graph theory.''