Social networks can be a very successful tool to engage users to discuss relevant topics for society. However, there are also some dangers that are associated with them, such as the emergence of polarization in online discussions. Recently, there has been a growing interest to try to understand this phenomenon, as some consider that this can be harmful concerning the building of a healthy society in which citizens get used to polite discussions and even listening to opinions that may be different from theirs. In this work, we face the problem of defining a precise measure that can quantify in a meaningful way the level of polarization present in an online discussion. We focus on the Reddit social network, given that its primary focus is to foster discussions, in contrast to other social networks that have some other uses. Our measure is based on two different characteristics of an online discussion: the existence of a balanced bipartition of the users of the discussion, where one partition contains mainly users in agreement (regarding the topic of the discussion) and the other users in disagreement, and the degree of negativity of the sentiment of the interactions between these two groups of users. We discuss how different characteristics of the discussions affect the value of our polarization measure, and we finally perform an empirical evaluation over different sets of Reddit discussions about diverse classes of topics. Our results seem to indicate that our measure can capture differences in the polarization level of different discussions, which can be further understood when analyzing the values of the different factors used to define the measure.

The bipartite polarization problem is an optimization problem where the goal is to find the highest polarized bipartition on a weighted and labeled graph that represents a debate developed through some social network, where nodes represent user’s opinions and edges agreement or disagreement between users. This problem can be seen as a generalization of the maxcut problem, and in previous work, approximate solutions and exact solutions have been obtained for real instances obtained from Reddit discussions, showing that such real instances seem to be very easy to solve. In this paper, we further investigate the complexity of this problem by introducing an instance generation model where a single parameter controls the polarization of the instances in such a way that this correlates with the average complexity to solve those instances. The average complexity results we obtain are consistent with our hypothesis: the higher the polarization of the instance, the easier is to find the corresponding polarized bipartition. In view of the experimental results, it is computationally feasible to implement transparent mechanisms to monitor polarization on online discussions and to inform about solutions for creating healthier social media environments.