I'm taking a Discrete mathematics course currently.
At the moment we're working with different algorithms to manipulate graphs and the neighbor matrix of graphs.
I'm trying to learn more about how to work with a specific algorithm but I'm not sure what it is called in English, would appreciate if someone could point me in the right direction, in Norwegish its called: Potensmetoden. A rough translation would be Power of method.
The method looks like: $$ M_{2} = \frac{N^{2}}{|N^{2}b|} $$
If I have something like a
$$ N = \begin{bmatrix} 0 & 1 & 0 & 1 & 1 & 1 \\ 1 & 0 & 1 & 1 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 \\ 1 & 1 & 1 & 0 & 1 & 1\\ 1 & 0 & 0 & 1 & 0 & 1 \\ 1 & 0 & 0 & 1 & 1 & 0 \end{bmatrix} $$
This would end up as
$$ N^{2} = N * N = \begin{bmatrix} 0 & 1 & 0 & 1 & 1 & 1 \\ 1 & 0 & 1 & 1 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 \\ 1 & 1 & 1 & 0 & 1 & 1\\ 1 & 0 & 0 & 1 & 0 & 1 \\ 1 & 0 & 0 & 1 & 1 & 0 \end{bmatrix} \begin{bmatrix} 0 & 1 & 0 & 1 & 1 & 1 \\ 1 & 0 & 1 & 1 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 \\ 1 & 1 & 1 & 0 & 1 & 1\\ 1 & 0 & 0 & 1 & 0 & 1 \\ 1 & 0 & 0 & 1 & 1 & 0 \end{bmatrix} = \begin{bmatrix} 4 &1 & 2 & 3 & 2 & 2 \\ 1 & 3 & 1 & 2 & 2 & 2 \\ 2 & 1 & 2 & 1 & 1 & 1 \\ 3 & 2 & 1 & 5 & 2 & 2 \\ 2 & 2 & 1 & 2 & 3 & 2 \\ 2 & 2 & 1 & 2 & 2 & 3 \end{bmatrix} $$
$$ \underbrace{\begin{bmatrix} 4 &1 & 2 & 3 & 2 & 2 \\ 1 & 3 & 1 & 2 & 2 & 2 \\ 2 & 1 & 2 & 1 & 1 & 1 \\ 3 & 2 & 1 & 5 & 2 & 2 \\ 2 & 2 & 1 & 2 & 3 & 2 \\ 2 & 2 & 1 & 2 & 2 & 3 \end{bmatrix}}_{N_{2}} \underbrace{\begin{bmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \end{bmatrix}}_{b} = \begin{bmatrix} 14 \\ 11 \\ 8 \\ 15 \\ 12 \\ 12 \end{bmatrix} $$
$$Norm |N_{2}b| = \sqrt{14^{2} + 11^{2} + 8^{2} + 15^{2} + 12^{2} + 12^{2}} \approx 29.9$$
$$ M_{2} = \frac{N^{2}}{|N^{2}b|} = \frac{1}{29.9} \begin{bmatrix} 4 &1 & 2 & 3 & 2 & 2 \\ 1 & 3 & 1 & 2 & 2 & 2 \\ 2 & 1 & 2 & 1 & 1 & 1 \\ 3 & 2 & 1 & 5 & 2 & 2 \\ 2 & 2 & 1 & 2 & 3 & 2 \\ 2 & 2 & 1 & 2 & 2 & 3 \end{bmatrix} \approx \begin{bmatrix} 0,138 & 0,033 & 0,067 & 0,100 & 0,067 & 0,067 \\ 0,033 & 0,100 & 0,033 & 0,067 & 0,067 & 0,067 \\ 0,067 & 0,033 & 0,067 & 0,033 & 0,033 & 0,033 \\ 0,100 & 0,067 & 0,033 & 0,167 & 0,067 & 0,067 \\ 0,067 & 0,067 & 0,033 & 0,067 & 0,100 & 0,067 \\ 0,067 & 0,067 & 0,033 & 0,067 & 0,067 & 0,100 \end{bmatrix} $$
An lastly, getting M_{2}b
$$ M_{2}b = \begin{bmatrix} 0,468 \\ 0,368 \\ 0,268 \\ 0,502 \\ 0,401 \\ 0,401 \end{bmatrix} $$
I understand this relatively alright, however, in the next task I shall build upon this method by taking it up to a power of 4 and there im lost, i figured it would be the same steps basiclly i went back and took N^4 and started over. But I didn't manage to finish it.
Method of the secound part of the task:
$$ M_{4} = \frac{N^{4}}{|N^{4}b|} = \frac{M^{2}_{2}}{|M^{2}b|}, M_{4}b $$
I think it's power iteration. See here. Is this what you're trying to do? You never mentioned what the algorithm you're referring to is for, but I think this is it.