# Random Walk with Restart vs. Personalized Pagerank

Are Personalized Pagerank and Random Walk with Restart really the same thing? From this source, it seems to be: http://web.eecs.umich.edu/~dkoutra/papers/fabp_pkdd2011.pdf

I've used the RANKS RWR function and the igraph personalized page.rank function and have gotten different results, but it is not clear to me why if they are the same. If they are different, how precisely are they different?

PPR:
Given a row-normalized adjacency matrix S, a scalar 0<=a<=1, and fixed vector u, find PPR vector v such that vT = vT [ (1-a) S + a*1.uT] here a is typically 0.25 -- with smaller probability walker jumps to nodes of personalization vector u.

RWR: Given a row-normalized adjacency matrix S, a scalar 0<=a<=1, and fixed vector u, find RWR vector w such that wT = wT (1-a) S + a*uT here a is typically 0.25 – with larger probability walker jumps to neighbours of current node.

• Ok, so from this it seems that they are identical. – Josh Nov 22 '17 at 19:01
• They are identical since vT.(1.uT)=(vT.1).uT=uT when ||v||_1=1. – Iraj Feb 2 '18 at 13:36