As page-rank is described in the original article, and in the wikipedia article, it is indeed not defined when out-degree(v)=0
for some v
, since you get P(v,u)=d/n+(1-d)*0/0
- which is undefined
A node that has no outgoing edge is called a dangling node and there are basically 3 common ways to take care of them:
- Eliminate such nodes from the graph (and repeat the process iteratively until there are no dangling nodes.
- Consider those pages to link back to the pages that linked to them (i.e. - for each edge
(u,v)
, ifout-degree(v) = 0
, regard(v,u)
as an edge). - Link the dangling node to all pages (including itself usually), and effectively make the probability for random jump from this node 1.
About a page with no incoming node - that shouldn't be an issue because everything is perfectly defined. Such a node will have a page rank of exactly d/n
- because you can only get to it by random surfing from any node - and that's the probability to be in it.
Hope that answered your question!