Understanding extreme events, such as hurricanes or forest fires, is of paramount importance because of their adverse impacts on human beings. Such events often propagate in space and time. Predicting - even a few days in advance - what locations will get affected by the event tracks could benefit our society in many ways. Arguably, simulations from first principles, where underlying physics-based models are described by a system of equations, provide least reliable predictions for variables characterizing the dynamics of these extreme events. Data-driven model building has been recently emerging as a complementary approach that could learn the relationships between historically observed or simulated multiple, spatio-temporal ancillary variables and the dynamic behavior of extreme events of interest. While promising, the methodology for predictive learning from such complex data is still in its infancy. In this paper, we propose a dynamic networks-based methodology for in-advance prediction of the dynamic tracks of emerging extreme events. By associating a network model of the system with the known tracks, our method is capable of learning the recurrent network motifs that could be used as discriminatory signatures for the event's behavioral class. When applied to classifying the behavior of the hurricane tracks at their early formation stages in Western Africa region, our method is able to predict whether hurricane tracks will hit the land of the North Atlantic region at least 10-15 days lead lag time in advance with more than 90% accuracy using 10-fold cross-validation. To the best of our knowledge, no comparable methodology exists for solving this problem using data-driven models.