Order of Stochasticity and Primitivity in Page Rank algorithm

In the Page Rank Algorithm does one apply the Stochasticity adjustment before 开发者_如何学Gothe Primitivity adjustment or the other way round.

Despite this being an old question, here it goes: Stochasticity before Primitivity. Page 37 and 38 of this article explain it well.

To summarize, just keep in mind what the overall goal is:

• Stochasticity: every row sums up to one (since these are transition probabilities)
• Primitivity: there are no non-zero elements in our matrix (every state is at least a little connected to every other state).

It is possible to do it the other way around, but this is less intuitive in my opinion. In that case you just have to normalize the rows (affecting only those that were empty before primitivity adjustment).

By the way, primitivity doesn't really require all elements to be non-zero, but in this case it's an obvious, easy and elegant way to ensure it.

Stochasticity adjustment should be before Primitivity Adjustment, the first one prevents the problem of RankSink which is the case of dangling nodes that absorb the whole importance of the web graph, the second one adds the teleportation matrix, which helps fulfill zero elements of the transition matrix to insure the primitivity of the resultant Google matrix, this helps preventing the problems of the reducibility and periodicity of the web graph.