It seems as though the algorithm converges with A > B because G doesn’t link to anything. As a result, on each pass, some of the total Page Rank is lost (i.e. it is collected by G, but not redistributed back into the network – this is not solved by the normalization…in fact, if you remove the normalization you will notice that is actually converging on all zeros). If G is removed from the network or links somewhere else, the system converges correctly (with or without normalization, although some normalization does appear to significantly increase the rate of convergence).

Problems also arise if two networks are connected in one direction only (i.e. G is connected to some node H, which is only connected back to G). All the Page Rank that flows into G gets trapped in G and H and never flows back out into the rest of the network. This is probably the idea that a lot of spammers use to try to get their page ranks up. Clearly, Google has solved this problem (I wonder how!).