Detecting Echo Chambers in social media; a graph-based approach =

Social media are becoming more and more popular and are used to discuss a wide range of topics. On these platforms we are often experiencing polarization between the users, producing a clear separation between groups with different opinions. Echo Chambers are closely related to this phenomenon: an Echo Chamber is a group of users with the same beliefs that reinforce their ideas. The growing complexity and quantity of online interactions requires us to find new techniques for detecting Echo Chambers. In this work we propose the Echo Chamber Problem (ECP) and the Densest Echo Chamber Problem (D-ECP), new formulations that take into account the concepts of content (the piece of information that is discussed) and thread (the "locality" discussing the content) in finding polarization. Our idea is that Echo Chambers correspond to groups of users discussing a content which is controversial, i.e. globally triggers many hostile interactions, with no controversy, i.e. with mainly friendly interactions inside the Echo Chamber. We will show that the problems we propose are hard to approximate within any non-trivial factor and propose Mixed Integer Programming (MIP) models and heuristics for solving them. Finally, we will focus on one of these methods and show that it is able to find Echo Chambers in synthetic data but has some limitations when applied to real-world data.