Brain networks consist of nodes that are anatomically defined brain regions, and edges that connect a pair of brain regions. The diffusion-weighted magnetic resonance images and the advances in computer-aided tractography algorithms showed that human brain networks are strongly associated with cognitive functions. Brain regions dedicated to a specific cognitive function are spatially clustered and efficiently connected each other; this is called local functional segregation. However, it is not well known that such a local segregation is associated with sub-networks which may act as building blocks of brain networks. In this work, we used machine learning techniques to analyze brain networks. Specifically, using an auto-encoder and a graph auto-encoder, we decomposed brain networks into several essential building blocks, and compared their results through various measures of decomposition quality. We observed that the graph auto-encoder out-performed the auto-encoder, and that its results showed significant correlation with cognitive deterioration in Alzheimer’s disease.