Exponential Ranking: Taking into Account Negative Links

Networks have attracted a great deal of attention the last decade, and play an important role in various scientific disciplines. Ranking nodes in such networks, based on for example PageRank or eigenvector centrality, remains a hot topic. Not only does this have applications in ranking web pages, it also allows peer-to-peer systems to have effective notions of trust and reputation and enables analyses of various (social) networks. Negative links however, confer distrust or dislike as opposed to positive links, and are usually not taken into account. In this paper we propose a ranking method we call exponential ranking, which allows for negative links in the network. We show convergence of the method, and demonstrate that it takes into account negative links effectively.