I'm reading some definition of page rank, in particular how page rank work on the web graph.
I'm a little bit confused about the definition of the teletransportation step.
How I understand this phase is if we have a Graph G with size N, the probability to be in each node is equally distributed so the probability is $\frac{1}{N}$.
So, if I got the point, the teletrasportation step on the rank function is the $\frac{1}{N}$ positioned in the last part of the formula, right?
$rank(i) = \alpha \cdot \sum_{j \in B(i)}{ \frac{rank(j)}{B(j)} + (1 - \alpha) \cdot \frac{1}{N} }$
I've seen more often the word teleportation.
The idea is to modify a bit the initial graph/matrix in order to be able to apply Perron-Frobenius theorem.
Usually, starting from the random walk matrix $H_{i,j} = \frac{1}{d^+(i)} \text{ if $i$ is connected to $j$}$; the first step is to get rid of the dead-ends by setting $S_{i,j} = \begin{cases} \frac{1}{d^+(i)} \text{ if $i$ is connected to $j$ and }{d^+(i)} >0 \\ {\frac{1}{n} \text{ otherwise }}\end{cases} $.
With this you get a stochastic matrix. Then you force the matrix to be aperiodic by adding a teleportation component $G = \alpha S + (1-\alpha)\frac{1}{n} J$ ($J$ is the all-one matrix). Doing so you get a stochastic aperiodic matrix and you can apply Perron Theorem.
I find this survey quite nice and helpful.