We suggest a new approach to estimate a brain network to model cognitive tasks and explore the node degree distribution of this network in anatomic regions. Functional Magnetic Resonance Images are used to estimate the relationship among the voxels. First, a local mesh is formed around each voxel in a predefined neighborhood system. Then, the edge weights of meshes, called Mesh Arc Descriptors (MAD) are estimated using a linear regression model. In order to estimate the optimal mesh size for voxels, the error term obtained during the estimation of Mesh Arc Descriptors are employed to optimize Akaike's Information Criterion. Finally, the brain network is constructed for each class by the estimated MAD. During experiments, we analyze how the degree of nodes varies across the anatomic brain regions for different cognitive states. Our results indicate that some anatomic regions make dense connections for all cognitive tasks whereas some of them have relatively sparse connections. This observation is consistent with the previously reported findings of anatomic regions. Although the degree distributions look similar for all classes, there are slight variations among classes. Therefore, the statistics of node degree distribution may be used to discriminate the anatomic regions related to cognitive tasks.