Analyzing the Influence of Agents in Trust Networks: Applying Nonsmooth Eigensensitivity Theory to a Graph Centrality Problem

Jon Donnelly, Peter Stechlinski

Abstract: Graph centrality measures have found widespread use ranking agents in networks by characterizing their “importance” for the purpose of predicting and managing network outcomes. One major application of such a graph centrality problem is found in decentralized, peer-to-peer networks; in particular, the EigenTrust algorithm for trust management aims to reduce the amount of malware distributed in peer-to-peer networks by using graph centrality as a metric for reputation. This popular scheme has been successfully applied to many different types of peer-to-peer networks. However, the effect malicious agents can have on the reliability of schemes like EigenTrust through overt or covert behavior has not yet been fully investigated. In this work, we analyze vulnerabilities in EigenTrust by extending classical eigenvalue/eigenvector sensitivity theory to the nonsmooth setting, where the presence of nonsmoothness in this problem arises from defense mechanisms built into EigenTrust. This enables us to compute the sensitivity of trust scores to ratings provided by individual agents, revealing vulnerabilities in EigenTrust. Our findings indicate that malicious agents can have a large impact on a network despite having relatively low centrality themselves (i.e., appearing untrustworthy).