Random surfing on multipartite graphs

Equipping an imaginary Random Surfer of the Web with the ability to teleport, was Page et al.'s creative way to justify a mathematical necessity; the Teleportation Matrix. Despite being essential for ensuring the ergodicity of the underlying Markov chain, the standard definition of this matrix treats the nodes of the graph in a simplistic and “leveling” way that can prove counterintuitive — especially for applications of the method on graphs of heterogeneous data. In this work, we focus on such graphs and we propose a novel alternative teleportation model that yields a well-defined ranking vector, while being as easy to handle as the traditional teleportation. We explore the theoretical implications of our model, and we reveal a wealth of nice properties that result to direct computational advantages over PageRank. We conduct a set of experiments using real-world datasets and we verify both the useful computational characteristics of our model and its favorable qualitative performance. Our promising findings suggest there remain more to be explored, and maybe much to be gained, by revisiting the teleportation model; a neglected part of PageRank that is typically taken for granted by the majority of applications in the literature.