Modeling and predicting people’s opinions plays an important role in today’s life. For viral marketing and political strategy design, it is particularly important to be able to analyze competing 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 "behaved" abnormally? Furthermore, can we predict how the opinions of individual users will change in the future? To answer such questions, it is insufficient to study individual user behavior, since opinions spread beyond users’ ego-networks. Instead, we need to consider the opinion dynamics of all users simultaneously.

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 opinion dynamics model. SND has a rich semantics of a transportation problem, yet, is computable in pseudo-linear time, thereby, being applicable to large-scale social networks analysis. We demonstrate the effectiveness of SND in experiments with Twitter data.