# 41 KAM Mathematical Colloquium

## Prof. HERBERT S. WILF

### University of Pennsylvania

## SEARCH ENGINES, EIGENVECTORS, AND CHROMATIC NUMBERS

May 4, 2001

## Abstract

A search engine can return a list of hits ranked in descending order of importance. How can they determine the importance of the web sites involved? The Kendall-Wei ranking scheme uses the Perron eigenvector of the matrix whose elements measure the influence of each site on the others. We will discuss this scheme, and the Perron-Frobenius theorem that underlies it. Applications will be given to web search, ranking of tournaments, football pools, etc.