The balance of synchrony and asynchrony, and the resulting complexity of the dynamics, has been quantified based on, e.g., the probability distribution of pairwise correlation between nodes (Zhao et al., 2010; Zamora-López et al., 2016), the probability distribution of joint states of nodes (Marshall et al., 2016), modularity analysis on the correlation matrix (Zhou et al., 2006; Zhao et al., 2011), and Granger causality analysis on the temporal pattern of joint states (Shanahan, 2008). Such measures have been applied not only to analyze synthetic networks but also anatomical brain connectomes, which revealed that the dynamical complexity is maximized therein (Zhao et al., 2010; Zamora-López et al., 2016). Most of the measures are applicable to phase oscillator systems, and their combination would provide a theoretical framework for further investigating the structure-function relationships within NoNs, such as brain networks.
