PolarityRank: Finding an equilibrium between followers and contraries in a network

In this paper we present the relevance ranking algorithm named PolarityRank. This algorithm is inspired in PageRank, the webpage relevance calculus method used by Google, and generalizes it to deal with graphs having not only positive but also negative weighted arcs. Besides the definition of our algorithm, this paper includes the algebraic justification, the convergence demonstration and an empirical study in which PolarityRank is applied to two unrelated tasks where a graph with positive and negative weights can be built: the calculation of word semantic orientation and instance selection from a learning dataset.