Science:Math Exam Resources/Courses/MATH307/April 2013/Question Section 201 06 (a)/Solution 1

When $\alpha$ = 0,

The stochastic matrix P is the sum of the outgoing links and the dangling links:

$P={\begin{bmatrix}0&0&0&0&0&1/6\\1/2&0&0&0&0&1/6\\0&1/2&0&0&0&1/6\\1/2&0&0&0&0&1/6\\0&1/2&0&1&0&1/6\\0&0&1&0&1&1/6\end{bmatrix}}$

Vertex 6 has no links leaving the site, so it is a dangling node. When the web surfer reaches a dangling node, we assume that any page on the internet can be chosen at random with equal probability. This is why all the entries in column 6 of matrix P contain the value 1/6.