That's not true. The page rank is read from the eigenvector, and is the value associated with the given vertex (ie web page). There are as many page rank values

That's not true. The page rank is read from the eigenvector, and is the value associated with the given vertex (ie web page). There are as many page rank values as there are web pages, but only one eigenvector from which to read: the dominant eigenvector of the transition matrix, which is the one with the largest eigenvalue. So, only a single eigenvalue for the entire pagerank computation.