Algorithms For Dummies

  Getting the Right Web page 

     219

The new function 

PageRank_naive

 wraps all the previously described operations 

and emits a vector of probabilities (the PageRank score) for each node in the 

 network. The third node emerges as the one with most importance. Unfortunately, 

the same function doesn’t work with the other two networks:

print(PageRank_naive(Graph_B))

Warning: G is substochastic

[ 0.  0.  0.  0.  0.  0.]

print(PageRank_naive(Graph_C))

[ 0.     0.     0.     0.222  0.444  0.333]

In the first case, the probabilities seem to drain out of the network — the effect of 

a dead-end website and the resulting substochastic transition matrix. In the 

 second case, the bottom half of the network unfairly gets all the importance, leav-

ing the top part as insignificant.