Although the previous formula is the one from the original paper, which introduced the PageRank algorithm in 1996, be aware that another one is sometimes used instead. In the original formula, the sum of ranks for all nodes adds up to N, which is the number of nodes. The updated formula is normalized to 1 instead of N and is written as follows:
PR(A) = (1 - d) / N + d * (PR(N1)/C(N1) + ... + PR(Nn)/C(Nn))
You can understand this easily by assuming that the ranks for all the nodes are initialized to 1/N. Then, at each iteration, each node will equally distribute this rank to all its neighbors so that the sum remains constant.
This formula was chosen for the PageRank implementation in networkx, the Python package for graph manipulation. However, Neo4j GDS uses the original formula. For this reason, in the following subsections, we are going to use the original version of the PageRank equation.
