That's easier explained using fixed-point theory: The damping factor makes the mapping x↦Sx into an actual contraction (on the space of probability distribution

That's easier explained using fixed-point theory: The damping factor makes the mapping x↦Sx into an actual contraction (on the space of probability distributions). Not to mention that it has a simple common-sense justification (you don't want to get stuck in a subnetwork that only links to itself, or drown out a subnetwork that has more outlinks than inlinks). There is probably some gain from understanding the algorithm specifically as a Markov chain iteration (if nothing else, it provides a great example for Markov chain iteration), but I think it's perfectly possible -- and easier -- to understand it as a fixed-point iteration on a compact space. And I am someone who does algebra for a living and normally explains everything algebraically if ever possible...