Discovering Polarization Niches via Dense Subgraphs with Attractors and Repulsers

Detecting niches of polarization in social media is a first step towards deploying mitigation strategies and avoiding radicalization. In this paper, we model polarization niches as close-knit dense communities of users, which are under the influence of some well-known sources of misinformation, and isolated from authoritative information sources. Based on this intuition we define the problem of finding a subgraph that maximizes a combination of ( i ) density, ( ii ) proximity to a small set of nodes A (named Attractors ), and ( iii ) distance from another small set of nodes R (named Repulsers ). Deviating from the bulk of the literature on detecting polarization, we do not exploit text mining or sentiment analysis, nor we track the propagation of information: we only exploit the network structure and the background knowledge about the sets A and R , which are given as input. We build on recent algorithmic advances in supermodular maximization to provide an iterative greedy algorithm, dubbed Down in the Hollow (dith), that converges fast to a near-optimal solution. Thanks to a novel theoretical upper bound, we are able to equip dith with a practical device that allows to terminate as soon as a solution with a user-specified approximation factor is found, making our algorithm very efficient in practice. Our experiments on very large networks confirm that our algorithm always returns a solution with an approximation factor better or equal to the one specified by the user, and it is scalable. Our case-studies in polarized settings, confirm the usefulness of our algorithmic primitive in detecting polarization niches.