In this study, we propose a new approach to construct a two-level functional brain network. The nodes of the first-level network are the voxels of the functional Magnetic Resonance Images (tMRI) recorded during an object recognition task. The nodes of the network at the second-level are the anatomic regions of the brain. The arcs of the first level are estimated by a linear regression equation for the meshes formed around each voxel. Neighbors of each voxel are determined by using a functional similarity metric. The node degree distributions of the voxel-level functional brain network are then used to estimate the node attributes and arc weights between the nodes of anatomic regions at the second level. The region-level functional brain network is then used to analyze the relationship among the anatomic regions of the brain during a cognitive process. Our results indicate that, although the neighborhood is defined functionally, voxels tend to make connections within the anatomic regions. Therefore, it can be deduced that nearby voxels work coherently during the cognitive task compared to the voxels apart from each other.