Question

Show the values obtained by applying two rounds of the Hubs and Author ities ranking procedure to the following network of web pages.

Answer 1

1st round of Hubs and Authorities ranking procedure:

Adjacency matrix representation of the graph is:

M=

	A	B	C	D	E
A	0	0	1	0	0
B	0	0	1	1	1
C	0	0	0	0	0
D	0	0	0	0	0
E	0	0	0	0	0

Transpose matrix of M

M^T =

	A	B	C	D	E
A	0	0	0	0	0
B	0	0	0	0	0
C	1	1	0	0	0
D	0	1	0	0	0
E	0	1	0	0	0

Assume the initial hub weight vector is:

u=

1

1

1

1

1

We compute the authority weight vector by:

v= M^T x u =

0	0	0	0	0
0	0	0	0	0
1	1	0	0	0
0	1	0	0	0
0	1	0	0	0

x

1

1

1

1

1

=

0

0

2

1

1

Then, updated hub weight is:

u = M x v =

0	0	1	0	0
0	0	1	1	1
0	0	0	0	0
0	0	0	0	0
0	0	0	0	0

x

0

0

2

1

1

=

2

4

0

0

0

Nodes	Hub(u)	Authority(v)
A	2	0
B	4	0
C	0	2
D	0	1
E	0	1

2nd round of Hubs and Authorities ranking procedure:

u = 2² + 4² + 0² + 0² + 0² = 20

=2/sqrt(20) , 4/sqrt(20), 0/sqrt(20), 0/sqrt(20), 0/sqrt(20)

=0.4472, 0.8944, 0, 0, 0

v= 0² + 0² + 2² + 1² + 1² = 6

= 0/sqrt(6), 0/sqrt(6), 2/sqrt(6), 1/sqrt(6), 1/sqrt(6)

=0, 0, 0.8165, 0.4082, 0.4082

Nodes	Hub(u)	Authority(v)
A	0.4472	0
B	0.8944	0
C	0	0.8165
D	0	0.4082
E	0	0.4082