> Before you could have invented PageRank, you must think in graphs.

For anyone puzzling over what is the graph-based perspective, there's actually a very elegant and simple mathematical way to derive page rank.

Define the directed graph of web links / citations through its adjacency matrix: web pages as nodes and links as directed edges. Represent a web surfer as a random walker on this graph, and run forth (simulate) the probability distribution of where they might end up.

If you've studied linear algebra you would see an immediate analogy between the PageRank algorithm how the power method is used to find the dominant eigenvector (of the transition matrix, which is a normalized version of the adjacency matrix).

This process is basically equivalent to implementing the diffusion process generated by the discrete graph laplacian. And simulating the random walk to find the long term stationary probability dstribution over nodes is akin to finding the zero eigenvector of this graph laplacian -- because it must generate "zero change" on the fixed point state.