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I am going to share the answer I've got from my professor. In the case of multiple eigenvalues, the exact analytical solution for the eigenvector contains a much greater degree of uncertainty than in the case of a non-multiple one. For a non-multiple eigenvalue, the eigenvector is defined up to its length, while its direction is determined uniquely, and the ...

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It's a bit late, but I have a very simple answer: there is nothing wrong with the code I was simply missing the extra optimisation that Newman recommends in his paper. The results are perfectly in-line with what is reported in the paper without applying the extra optimisation step. I'll leave this up in case it helps someone implementing the algorithm.

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When one says an algorithm is of order $O(n)$, that may mean that the complexity is given by: $c + b*n$. With every new element you add you increase in runtime (effectively). What mathematically minded people often forget is that these statements do not include how large the constants are. That of course carries over to $O(n²)$ and such. I can not answer ...

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