Abstract
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 (EO and 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.