Network properties of healthy and Alzheimer brains

The application of graph theory in diffusion weighted resonance magnetic images have allowed the description of the brain as a complex network, often called structural network. For many years, the small-world properties of brain networks have been studied and reported. However, few studies have gone beyond of clustering and characteristic path length. In this work, we compare the structural connection network of a healthy brain and a brain affected by Alzheimer’s disease with artificial small-world networks. Based on statistical analysis, we demonstrate how artificial networks can be constructed using Newman–Watts procedure. The network quantifiers of both structural matrices are identified inside a probabilistic valley. Despite of similarities between structural connection matrices and artificial small-world networks, increased assortativity can be found in the Alzheimer brain. Due to limited experimental data, we cannot define a direct link between Alzheimer’s disease and assortativity. Nevertheless, we intend to call attention for an important network quantifier that has been neglected. Our results indicate that network quantifiers can be helpful to identify abnormalities in real structural connections, for instance Alzheimer’s disease that disrupts the communication among neurons. One of our main results is to show that the network indicators of the Alzheimer brain are almost identical with the small-world network, except the assortativity.