For the following graph

which of the following algorithms could be used for ranking the nodes?

If a matrix A can be written as 

then what is the pseudo-inverse of A ?

Suppose we have three vectors x, y and z all of which are the same length. We wish to perform a least squares fit where we can write 

what must one minimise?  

A graph with 4 nodes has the following diffusion matrix. The nodes are labelled 1 to 4. 

P .

The first row represents transition probabilities for node 1 and so on.

We wish to compute the ranking of these sites using the diffusion algorithm. We will assume that the initial vector representation is 

(i.e. We are assuming we are initially on node 3).  What is the vector representation after one iteration of the diffusion algorithm?