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I've been recently working with graph sampling, and I can't seem to find useful explanation of the following two aspects. On one side there are pagerank-based algorithms, which converge to a stationary distribution, and are extremely useful for modern graph mining tasks.

On the other hand, many network embedding methods leverage $1^{st}$ or $2^{nd}$ order random walks for network sampling.

I am wondering what is the exact connection between the two? Is pagerank actually a form of a $2^{nd}$ order graph walk?

Thank you!

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After some reading: P-PR and similar algorithms are described by first order Markovian dynamics, as doing higher orders becomes analytically untractable (e.g., network embedding algorithms need to do sampling).

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