So first of all, the PageRank value of a node after k steps can be interpreted as

the probability that a random walker lands on that node after taking k random steps.

And so having said that, let me tell you what a random walk is.

Let's think about a random walk of k steps.

The way it works is that you would start on a random node, and then you're going to

choose outgoing edges at random, and follow those edges to the next node.

And then you're going to repeat this k times.

So, for example, let's take a random walk of five steps in this graph.

So first, you would choose some random node, let's say you chose node D.

And now, you're going to choose one random edge going from D to another node.

So there are three options here.

Let's say you chose the one going to node A.

So then, for your first step, you're going to walk from D to A.

And then you are going to repeat this four more times.

So you're going to choose a random edge going out from A, in this case,

there are no options.

The only one you can choose is the one going to B, so you follow it and

you go to node B.

And then you choose again a random edge, and

there are two options, either go to C or go to D.

Let's say you go to C, that's your Step 3.

Then out of C, there's only one edge,

you have to go back to B so you go back to B, that's Step 4.

And then we're back at B, you choose again randomly between going to C and D.

You may go to C again or maybe you go to D.

In this case, you went to D, and that's your fifth step.

So that's a random walk.

You simply randomly choose edges and walk along in the network.