In order to understand what PageRank is doing, let's compare the results of degree centrality and the PageRank algorithms on our small directed graph. This comparison is shown in the following table:
Node | Degree centrality | PageRank centrality |
A | 2 | 1.44 |
B | 1 | 1.52 |
C | 1 | 0.15 |
D | 1 | 0.76 |
While node A has the highest outgoing degree (2), it receives only one link, meaning only one other page in the graph trusts it. On the other hand, node B has an outgoing degree of 1, but three other pages of the network are pointing to it, giving it more credibility. That's the reason why, with PageRank centrality, the most important node is now node B.