Social networks influence health-related behaviors, such as obesity and smoking. While researchers have studied social networks as a driver for diffusion of influences and behaviors, it is less understood how the structure or topology of the network, in itself, impacts an individual's health behaviors and wellness state. In this paper, we investigate whether the structure or topology of a social network offers additional insight and predictability on an individual's health and wellness. We develop a model called the Network-Driven health predictor (NetCARE) that leverages features representative of social network structure. Using a large longitudinal data set of students enrolled in the NetHealth study at the University of Notre Dame, we show that the NetCARE model improves the overall prediction performance over the baseline models -- that use demographics and physical attributes -- by 38%, 65%, 55%, and 54% for the wellness states -- stress, happiness, positive attitude, and self-assessed health -- considered in this paper.