Resting-state brain networks (RSNs) have been recently used extensively for different tasks such as age prediction and patient classification. These networks are identified through analysis of synchronous low-frequency fluctuations in blood oxygenation level dependent (BOLD) signals obtained from resting-state functional magnetic resonance imaging (fMRI) scans. A significant majority of studies published so far involve time series analysis of fMRI signals to identify their endpoint of interest and less research has analyzed the connection between spatial networks of the brain to discover novel biomarkers. In this study, we show, for the first time, that the interaction between RSNs can uniquely characterize individual subjects. We propose a novel approach called BrainNet, a deep Siamese-based 3D convolutional neural network that learns to compare subjects by capturing the interactions between brain networks. We show that, our trained model can accurately discriminate subjects using pairs of networks as input and that it generalizes to the unseen cases. We also show the proposed model captures age-and gender-rich features in characterizing patterns of network-network interactions notwithstanding any supervision.