Graph Ranking and the Cost of Sybil Defense

TL;DR

This paper analyzes the vulnerability of ranking algorithms like PageRank to spam attacks, introduces a game-theoretic framework, and demonstrates that Min-PPR, used by Google, offers better spam resistance and low distortion.

Contribution

It characterizes the spam-rankers game, evaluates existing ranking functions, and provides a theoretical analysis showing Min-PPR's advantages in spam resistance and distortion.

Findings

Most ranking functions have poor spam resistance or high distortion.

Min-PPR has low distortion and high spam resistance.

Min-PPR includes a cost function highlighting vulnerable nodes.

Abstract

Ranking functions such as PageRank assign numeric values (ranks) to nodes of graphs, most notably the web graph. Node rankings are an integral part of Internet search algorithms, since they can be used to order the results of queries. However, these ranking functions are famously subject to attacks by spammers, who modify the web graph in order to give their own pages more rank. We characterize the interplay between rankers and spammers as a game. We define the two critical features of this game, spam resistance and distortion, based on how spammers spam and how rankers protect against spam. We observe that all the ranking functions that are well-studied in the literature, including the original formulation of PageRank, have poor spam resistance, poor distortion, or both. Finally, we study Min-PPR, the form of PageRank used at Google itself, but which has received no (theoretical or empirical) treatment in the literature. We prove that Min-PPR has low distortion and high spam resistance. A secondary benefit is that Min-PPR comes with an explicit cost function on nodes that shows how important they are to the spammer; thus a ranker can focus their spam-detection capacity on these vulnerable nodes. Both Min-PPR and its associated cost function are straightforward to compute.