Functional brain networks in Alzheimer’s disease: EEG analysis based on limited penetrable visibility graph and phase space method

• Complex network theory is applied to EEG series to study nonlinear characteristic.
• Functional brain connectivity is constructed from clustering coefficient sequences.
• Effective techniques are developed to explore features of functional brain network.
• The abnormalities of brain connectivity are investigated from AD patients.

In this paper, EEG series are applied to construct functional connections with the correlation between different regions in order to investigate the nonlinear characteristic and the cognitive function of the brain with Alzheimer’s disease (AD). First, limited penetrable visibility graph (LPVG) and phase space method map single EEG series into networks, and investigate the underlying chaotic system dynamics of AD brain. Topological properties of the networks are extracted, such as average path length and clustering coefficient. It is found that the network topology of AD in several local brain regions are different from that of the control group with no statistically significant difference existing all over the brain. Furthermore, in order to detect the abnormality of AD brain as a whole, functional connections among different brain regions are reconstructed based on similarity of clustering coefficient sequence (CCSS) of EEG series in the four frequency bands (delta, theta, alpha, and beta), which exhibit obvious small-world properties. Graph analysis demonstrates that for both methodologies, the functional connections between regions of AD brain decrease, particularly in the alpha frequency band. AD causes the graph index complexity of the functional network decreased, the small-world properties weakened, and the vulnerability increased. The obtained results show that the brain functional network constructed by LPVG and phase space method might be more effective to distinguish AD from the normal control than the analysis of single series, which is helpful for revealing the underlying pathological mechanism of the disease.