A brain network is the essence of the intelligence where it consists of nodes that are anatomically defined brain regions, and edges that connect a pair of brain regions. The diffusion-weighted magnetic resonance (MR) images and the advances in computer-Aided tractography algorithms let us know strong association between human brain networks and cognitive functions. Brain regions dedicated to a certain specific cognitive function were spatially clustered and efficiently connected each other; it is called local functional segregation. However, it is not well known that such a local segregation is associated with a certain sub-network which may act as a building block of the brain network. In this work, using a graph auto-encoder, we extracted building blocks of brain networks and investigate whether they are affected by a neurological disease, Alzheimer's disease. We found that the brain network of each person is linear summation of the learned building blocks. Also, the activation levels of these building blocks vary in the normal controls and patients with Alzheimer's disease, showing that network deterioration in the disease group.