  Analysis of opinion dynamics in social networks plays an important role in
today's life. For applications such as predicting users' political preference,
it is particularly important to be able to analyze the dynamics of competing
opinions. While observing the evolution of polar opinions of a social network's
users over time, can we tell when the network "behaved" abnormally?
Furthermore, can we predict how the opinions of the users will change in the
future? Do opinions evolve according to existing network opinion dynamics
models? To answer such questions, it is not sufficient to study individual user
behavior, since opinions can spread far beyond users' egonets. We need a method
to analyze opinion dynamics of all network users simultaneously and capture the
effect of individuals' behavior on the global evolution pattern of the social
network.
  In this work, we introduce Social Network Distance (SND) - a distance measure
that quantifies the "cost" of evolution of one snapshot of a social network
into another snapshot under various models of polar opinion propagation. SND
has a rich semantics of a transportation problem, yet, is computable in time
linear in the number of users, which makes SND applicable to the analysis of
large-scale online social networks. In our experiments with synthetic and
real-world 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. When employed for opinion prediction in Twitter,
our method's accuracy is 75.63%, which is 7.5% higher than that of the next
best method.
  Source Code: https://cs.ucsb.edu/~victor/pub/ucsb/dbl/snd/
