Black hole metric: Overcoming the pagerank normalization problem

In network science, there is often the need to sort the graph nodes. While the sorting strategy may be different, in general sorting is performed by exploiting the network structure. In particular, the metric PageRank has been used in the past decade in different ways to produce a ranking based on how many neighbours point to a specific node. PageRank is simple, easy to compute and effective in many applications, however it comes with a price: as PageRank is an application of the random walker, the arc weights need to be normalized. This normalization, while necessary, introduces a series of unwanted side-effects. In this paper, we propose a generalization of PageRank named Black Hole Metric which mitigates the problem. We devise a scenario in which the side-effects are particularily impactful on the ranking, test the new metric in both real and synthetic networks, and show the results.