Question

Figure 5.1: A hypothetical example of the Web

Exercise 5.5.1 : Compute the hubbiness and authority of each of the nodes in
our original Web graph of Fig. 5.1.

Could you provide the solution to me step by step?

Material Reference

http://infolab.stanford.edu/~ullman/mmds/ch5.pdf

Answer 1

Hubs and Authorities:

• It was proposed after page rank was implemented.
• It deals with iterative computation of fixed point involving repeated matrix vector multiplication.
• We can compute hubs and authorities using HITS(Hyperlink Induced Topic Search) algorithm.
• A good hub represents a page that pointed to many other pages.
• A good authority represented a page that was linked by many different hubs.

To identify the best hub and authority for the given graph calculate the hubs and authority score using hits algorithm for K=3.

Here K is number of iterations.

Procedure:

• First calculate the adjacency matrix for the given web graph.
• Later find the transpose of the adjacency matrix.
• Now assume initial hub weight vector,u as 1.
• calculate authority weight vector ,v

                                         v=transpose of the adjacency matrix * u(updated)

• Now calculate the updated hub weight vector ,u = adjacency matrix * v
• Now repeat it for the next two iterations.
• We can stop the iterations until the values of hubs and authorities remains same.

Given rophix groph is, Step (1) :- Calculate adlarency matuiv adatent the 0 Step fo- Calculale tvanxpose of a mabuiv, T D111 Sp/3)Aume nal hub wuighl vedo, u as 1 weu calculate authơily weght wdo (v) and hub w'g

10o hub weight vectas , u v 100 1 raph 4 2

(alculate new authority fomr -16 2 丁て 0バー Calculak new hub fom 匕 I 2 ㄐ 2. 爪爪爪GL 0.40 ) 0.4 ) 0,33 ) 0,47 o 23

Colcutate nwauthity am o-s , o,s, o,s, o. 5 , o- S alcutale new hub tom r 98 0

Hニ0,23

The values of hubs and authorities are same for k=2 and 3, so we can stop the iterations.

Here H- hub

A-authority