Synchrony and complexity in state-related EEG networks: an application of spectral graph theory

To characterize differences between different state-related brain networks, statistical graph theory approaches have been employed to identify informative, topological properties. However, dynamical properties have been studied little in this regard. Our goal here was to introduce spectral graph theory as a reliable approach to determine dynamic properties of functional brain networks and to find how topological versus dynamical features differentiate between such networks. To this goal, 45 participants performed no task with eyes open (EO) or closed (EC) while electroencephalography data were recorded. These data were used to create weighted adjacency matrices for each condition (rest state EO and rest state EC). Then, using the spectral graph theory approach and Shannon entropy, we identified dynamical properties for weighted graphs, and we compared these features with topological aspects of graphs. The results showed that spectral graph theory can distinguish different state-dependent neural networks with different synchronies. On the other hand, correlation analysis indicated that although dynamical and topological properties of random networks are completely independent, these network features can be related in the case of brain generated graphs. In conclusion, the spectral graph theory approach can be used to make inferences about various state-related brain networks, for healthy and clinical populations.\n\nAuthor SummeryBy considering functional communications across different brain regions, a complex network is achieved that is known as functional brain network. Topologically, this network is constructed by different nodes (activity of brain regions or signals over recording electrodes) and different edges (similarity, correlation or phase difference between nodes). Paths, clusters, hubs, and centrality of nodes are examples of topological properties of these networks. However, synchrony and stability of functional brain networks can not be revealed by consideration of topological properties. Alternatively, spectral graph theory (SGT) can demonstrate the dynamic, synchrony and stability of graphs. But this approach has been studied little in brain network analysis. Here, we employed SGT, as well as topological methods, to investigate which approaches are more reliable to find differences between distinct state-related brain networks. On the other hand, we investigated correlations between topology and dynamic in different type of networks (brain generated and random networks). We found that SGT measures can clearly distinguish between distinct state-related brain networks and it can reveal synchrony and complexity of these networks. Also, results show that although dynamic and topology of random-generated graph are completely independent, these properties exhibit several correlations in the case of functional brain networks.