And then the other rule is the Hub Update Rule,

which is sort of the symmetric thing.

So each node's hub score is going to be the sum of the authority scores

of each node that it points to.

And then we're going to have to do some normalizations because these scores

are going to keep growing and growing, so

at every iteration we're going to normalize the hub and the authority score.

And so, for example, the way you normalize the authority score is you take each

node's authority score, let's say j, and you divide the authority score of

j by the sum of all the authorities in the whole network.

And then we're going to repeat this process eight times.

Now, this might seem a little abstract at this point but

let's run through an example to see exactly how it works.

So we're going to take the network that we had just discussed,

and we're going to compute two iterations of the HITS algorithm of the network.

So just like in PageRank, we're going to have to keep track of the old

scores to be able to compute the new scores.

And because the first step is to give every node a hub and

authority score of one, we're going to start there.

We're going to give every node an old authority on hub score of 1,

and then we're going to compute the new scores.

So let's start with the authority scores.

We look at node A and we're going to look at what nodes point to node A in order to

figure out what the new authority score of A is, and

it turns out that C, G, and H point to A.

And because C, G, and H all have hub score of 1,

then the new authority score of A is going to be 3.

Next, node B, nodes D and E point to B, and E and D both have hub score of 1,

so B is going to have a new authority score of 2.

So you can see at this point that what we're really doing when we get this new

authority score is looking at the in-degree of each one of the nodes, and

that's what's going to happen.

So, for example, node C has an in-degree of 5.

And because all the nodes at this point have a hub score of 1,

then C is going to have a new authority score of 5.

And then D has two nodes pointing to it, so it has a new authority score of 2.

And E has in-degree of 1, F has in-degree of 1.

G has in-degree of 0, so it's going to have a new authority score of 0.

And H has one node pointing to it, so it has a new authority score of 1.

Okay, now let's move to the new hub scores.

It's going to be very similar, but now instead of looking at the in-degree

of every node, we're going to look at the auth degree.

And so, for example, A has an auth degree of 1, it points to D.

And now we have to look at these old authority score.

And again, because this is our first step,

every node has an old authority score of 1.

And D does as well, and so A is going to have a new hub score of 1.

B points to two things, both of them have an authority score of 1,

and so B has hub score of 2.

C has an auth degree of 1, so it has a new hub score of 1.

D has an auth degree of 2.

E has an auth degree of 4.

F has an auth degree of 2.

G has auth degree 2, and H has auth degree 1.