Twin study is one of the major parts of human brain research that reveals the importance of environmental and genetic influences on different aspects of brain behavior and disorders. Accurate characterization of identical and fraternal twins allows us to infer on the genetic influence in a population. In this paper, we propose a novel pair-wise classification pipeline to identify the zygosity of twin pairs using the resting state functional magnetic resonance images (rs-fMRI). The new feature representation is utilized to efficiently construct brain network for each subject. Specifically, we project the fMRI signal to a set of cosine series basis and use the projection coefficients as the compact and discriminative feature representation of noisy fMRI. The pair-wise relation is encoded by a set of twin-wise correlations between functional brain networks across brain regions. We further employ hill climbing variable selection to identify the most genetically affected brain regions. The proposed framework has been applied to 208 twin pairs in Human Connectome Project (HCP) and we achieved 92.23(±4.43)% classification accuracy.