I am using a different idea with PP. First off, it's a monte-carlo version, so I am simulating a bunch of random walks.

Secondly, I've added a new stopping rule: break the walk when a cycle is found.

example: a walk is a bunch of IDs of nodes, like {1, 11, 234, 7, 0}

The walk {1,2,1,2,1,2} contains cycles, so it's stopped earlier at {1,2}. This means 1 and 2 gets visited less often.

Cycles are really improbable for normal users, but highly probable for spam networks. The net result that I've found is basically no change for normal people, and a big de-rank for such networks (their scores go down by a factor of ~3)

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I would have expected cycles to be pretty common for normal users. Many of my follows follow each other and also follow me back.

yeah, but follows in random walks.

You see, nodeA follows 100 others. If each of these follows, follow him back and other 99 nodes

then the probability of doing nodeA --> follow --> nodeA is 1/100

Are you saying (or assuming) that when you encounter an army of N bots, then the bot army tends to be more tightly integrated than an organic group of normal users, bc the bot army strategy is for every bot to follow every other bot? Could a more sophisticated bot army then decide not to do this?

I suppose one way to understand why cycles are bad is that you get paths that are infinitely long. GrapeRank addresses this problem using a parameter called attenuation factor, aF, a number between 0 and 1. For any given path starting with the reference user, the weight of each successive hop is multiplied by aF. So the impact of a node that is N hops away on a given path is reduced by aF^N.