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The Second Eigenvalue of the Google Matrix [dbpubs.stanford.edu]
[quote] From the abstract:
We determine analytically the modulus of the second eigenvalue for the web hyperlink matrix used by Google for computing PageRank. Specifically, we prove the following statement: ``For any matrix $A=[cP + (1-c)E]^T$, where $P$ is an $n \times n$ row-stochastic matrix, $E$ is a strictly positive $n \times n$ rank-one row-stochastic matrix, and $0 \leq c \leq 1$, the second eigenvalue of $A$ has modulus $¦\lambda_2¦ \leq c$. Furthermore, if $P$ has at least two irreducible closed subsets, the second eigenvalue $\lambda_2 = c$.'' This statement has implications for the convergence rate of the standard PageRank algorithm as the web scales, for the stability of PageRank to perturbations to the link structure of the web, for the detection of Google spammers, and for the design of algorithms to speed up PageRank.[/url]
Craig
Spam Detection. The eigenvectors corresponding to the second eigenvalue ,are an artifact of certain structures in the web graph. In particular, each pair of leaf nodes in the SCC graph for the chain corresponds to an eigenvector of $ with eigenvalue.
These leaf nodes in the SCC are those subgraphs in the web link graph which may have incoming edges, but have no edges to other components. Link spammers often generate such structures in attempts to hoard rank. Analysis of the nonprincipal eigenvectors of may lead to strategies for combating link spam.
from Googleguy in: [webmasterworld.com...]
It's pretty easy to spot domains that are hoarding PageRank; that can be just another factor in scoring
just to make you all paranoid..(it does say may though...;)
