Analysis of opinion dynamics in social networks plays an important role in today's life. For predicting users' political preference, it is particularly important to be able to analyze the dynamics of competing polar opinions, such as pro-Democrat vs. pro-Republican. While observing the evolution of polar opinions in a social network over time, can we tell when the network evolved abnormally? Furthermore, can we predict how the opinions of the users will change in the future? To answer such questions, it is insufficient to study individual user behavior, since opinions can spread beyond users' ego-networks. Instead, we need to consider the opinion dynamics of all users simultaneously and capture the connection between the individuals' behavior and the global evolution pattern of the social network.

In this work, we introduce the Social Network Distance (SND)---a distance measure that quantifies the likelihood of evolution of one snapshot of a social network into another snapshot under a chosen model of polar opinion dynamics. SND has a rich semantics of a transportation problem, yet, is computable in time linear in the number of users and, as such, is applicable to large-scale online social networks. In our experiments with synthetic and Twitter data, we demonstrate the utility of our distance measure for anomalous event detection. It achieves a true positive rate of 0.83, twice as high as that of alternatives. The same predictions presented in precision-recall space show that SND retains perfect precision for recall up to 0.2. Its precision then decreases while maintaining more than 2-fold improvement over alternatives for recall up to 0.95. When used for opinion prediction in Twitter data, SND's accuracy is 75.6%, which is 7.5% higher than that of the next best method.