PROBLEM $3$

In this problem you are required to compare two versions of the HITS algorithm discussed in our lectures.

Figure $1-$ HITS Version $1$

Initialize all weights to $1.$

Repeat until convergence

$O$ operation : hubs collect the weight of the authorities

$h_i^t={\displaystyle \underset{j\text{:}ij}{\overset{?}{}}}{a}_j^{t-1}$

I operation: authorities collect the weight of the hubs

$a_i^t={\displaystyle \underset{j\text{:}ji}{\overset{?}{}}}{h}_j^{t-1}$

Normalize weights under some norm

Figure $2-$ HITS Version $2$

Initialize all weights to $1.-$ Repeat until convergence

$O$ operation : hubs collect the weight of the authorities

$h_i^t={\displaystyle \underset{j\text{:}ij}{\overset{?}{}}}{a}_j^{t-1}$

I operation: authorities collect the weight of the hubs

$a_i^t={\displaystyle \underset{j\text{:}ji}{\overset{?}{}}}{h}_j^t$

Normalize weights under some norm

You will pick $3$ graphs $($of your choice$)$ and a scale of tolerance of your choice and the comparison will be done in two aspects:

The hub and authority values that the algorithms converge to

The number of steps that the convergence is achieved

Note: in this problem you are not allowed to use any libraries.