Talk:Eigenvector centrality

There seem to be a couple of lapses in the reasoning:

• The Perron-Frobenius theorem guarantees that the largest eigenvalue is simple when the coefficients are > 0, but not if they are ≥ 0. It is obvious that this theorem does not hold with ≥ 0; consider the 2×2 identity matrix, it has (1 2) and (2 1) as positive eigenvectors for eigenvalue 1. Thus, there are many eigenvectors that are solutions, including multiple eigenvectors with 1-norm 1.
• However, the additional requirement that all the entries in the eigenvector be positive implies (by the Perron–Frobenius theorem) that only the greatest eigenvalue results in the desired centrality measure. I may have missed a point here, but while the Perron-Frobenius theorem guarantees that the largest eigenvalue has a positive eigenvector, it does not seem to guarantee that only the largest eigenvalue has a positive eigenvector. David.Monniaux 00:15, 8 December 2006 (UTC)

"Eigenvector+centrality" listed at Redirects for discussion

The redirect Eigenvector+centrality has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2025 November 6 § Eigenvector+centrality until a consensus is reached. Steel1943 (talk) 20:29, 6 November 2025 (UTC)