ARM4SNS:ReputationFunctions

PageRank

• $P$: set of hyperlinked webpages
  
• $u,v$: webpages in P
  
• $N^{-}(u)$: set of webpages pointing to u
  
• $N^{+}(v)$: set of webpages that v points to
  
• the PageRank is: $R(u)=cE(u)+c\sum _{v\in N^{-}(u)}\frac{R(v)}{|N^{+}(v)|}$ (1.)
• $c$ is chosen such that $\sum _{u\in P}R(u)=1$
  
• $E$ is a vector over $P$ corresponding to a source of rank and is chosen such that $\sum _{u\in P}E(u)=0.15$
  
• first term of function (1.) $cE(u)$ gives rank value based on initial rank
  
• second term of (1.) $c\sum _{v\in N^{-}(u)}\frac{R(v)}{|N^{+}(v)|}$ gives rank value as a function of hyperlinks pointing at $u$