Resting-state functional MRI (rs-fMRI) in functional neuroimaging techniques have accelerated progress in brain disorders and dysfunction studies. Since, there are the slight differences between healthy and disorder brain, investigation in the complex topology of functional brain networks in human is difficult and complicated task with the growth of evaluation criteria. Recently, graph theory and deep learning applications have spread widely to understanding human cognitive functions that are linked to gene expression and related distributed spatial patterns. Irregular graph analysis has been widely applied in many brain recognition domains, these applications might involve both node-centric and graph-centric tasks. In this paper, we discuss about individual Variational Autoencoder (VAE) and Graph Convolutional Network (GCN) for the region of interest recognition areas of brain which not have normal connection when apply certain tasks. Here in, we identified a framework of Graph Auto-Encoder (GAE) with hypersphere distributer for functional data analysis in brain imaging studies that is underlying non-Euclidean structure, in learning of strong rigid graphs among large scale data. In addition, we distinguish the possible mode correlations in abnormal brain connections.