Questions about ranking theory

Hello

I hav a question about the ranking theory (the thing Google
uses to rank webpages). I'm not quite informed about the
subject, so I think the algorithm is as following:

A:=incidence matrix of the oriented graph (V=pages,E=links)
V:=eigenvector of A corresponding to largest real eigenvalue

then, V contains some measure of the rank.

However, I have some questions about that

1) is it right?
2) how do I know that A will have real eigenvalues, and the
corresponding eigenvector will be positive (what would mean
neagtive rank?)
3) I was told it can be used for ranking soccer teams too.
However, when I think of a situation when

A defeated B
B defeated A
C defeated A

the eigenvector in question is (1,1,1). However, one would
say that team C is better than A,B. Is there some ranking
algorithm that would consider the verticies appearing sooner
in the topological ordering of the graph better (or worse, it
depends on the situation) than others?
4) Are there any references on the topic?

I'd be grateful for any answers

Jiri Palecek

.

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