Brain is constituted of large number of neuronal elements that suggests formidably complicated structural network. The anatomical substrate supports the dynamic emergence of coherent physiological activity of neurons that can span the multiple spatially distinction brain region of functional network. The approach based on graph theory to the complex network analysis is a powerful way of quantifying the brain’s structure and functional systems. Research highlights include the topological characteristics of brain structural and functional network, which based on distinct physiological and pathological states; the relation between neuronal dynamics and functional emergence of brain; and the prediction estimation from structural network to functional network. Figures describe the connectivity of regions of interest (ROIs) that suggests the specific function of brain, and the network cores that suggest the distinct importance of ROIs.