on the self-link issue.. (qn 5 in homework)

The question 5 in homework has two nodes that have outgoing links but those links point back to the pages themselves.

So the question is whether these pages are to be considered sink pages or not. 

One reasonable interpretation would be to consider them sink pages--since there is no way of leaving those pages and go anywhere else.

However, the specific "repair" we have for sink pages only works if we consider a page to be a sink page ONLY IF IT HAS NO OUTGOING LINKS

(not even links pointing back to itself). Otherwise, the repair will leave you with a probability mass of more than 1.0 on the outgoing links.

So, for this problem, you have to consider these self-looping pages as non-sink pages (despite the obvious fact that you can't leave them ;-).

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On a related note, although pagerank approach has been developed with Z and K matrices, if you are planning to use a uniform reset matrix, then in a way the sink page repair is superfluous (basically after the K matrix is added,  you will have an irreducible matrix already). 

Rao