The brain may be considered as a synchronized dynamic network with several coherent dynamical units. However, concerns remain whether synchronizability is a stable state in the brain networks. If so, which index can best reveal the synchronizability in brain networks? To answer these questions, we tested the application of the spectral graph theory and the Shannon entropy as alternative approaches in neuroimaging. We specifically tested the alpha rhythm in the resting-state eye closed (rsEC) and the resting-state eye open (rsEO) conditions, a well-studied classical example of synchrony in neuroimaging EEG. Since the synchronizability of alpha rhythm is more stable during the rsEC than the rsEO, we hypothesized that our suggested spectral graph theory indices (as reliable measures to interpret the synchronizability of brain signals) should exhibit higher values in the rsEC than the rsEO condition. We performed two separate analyses of two different datasets (as elementary and confirmatory studies). Based on the results of both studies and in agreement with our hypothesis, the spectral graph indices revealed higher stability of synchronizability in the rsEC condition. The k-mean analysis indicated that the spectral graph indices can distinguish the rsEC and rsEO conditions by considering the synchronizability of brain networks. We also computed correlations among the spectral indices, the Shannon entropy, and the topological indices of brain networks, as well as random networks. Correlation analysis indicated that although the spectral and the topological properties of random networks are completely independent, these features are significantly correlated with each other in brain networks. Furthermore, we found that complexity in the investigated brain networks is inversely related to the stability of synchronizability. In conclusion, we revealed that the spectral graph theory approach can be reliably applied to study the stability of synchronizability of state-related brain networks.

中文翻译：

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状态相关脑电图网络中的同步性和复杂性：谱图理论的应用

大脑可以被认为是一个同步的动态网络，具有几个连贯的动态单元。然而，人们仍然担心同步性是否是大脑网络中的稳定状态。如果是这样，哪个指标最能揭示大脑网络的同步性？为了回答这些问题，我们测试了谱图理论和香农熵作为神经成像替代方法的应用。我们专门测试了静息态闭眼 (rsEC) 和静息态睁眼 (rsEO) 条件下的 alpha 节律，这是神经影像脑电图同步的一个经过充分研究的经典例子。由于 rsEC 期间 alpha 节律的同步性比 rsEO 更稳定，我们假设我们建议的谱图理论指数（作为解释大脑信号同步性的可靠措施）应该在 rsEC 中表现出比 rsEO 条件更高的值。我们对两个不同的数据集进行了两次单独的分析（作为基础研究和验证性研究）。基于两项研究的结果并与我们的假设一致，光谱图指数显示在 rsEC 条件下同步性具有更高的稳定性。k-mean 分析表明，谱图指数可以通过考虑大脑网络的同步性来区分 rsEC 和 rsEO 条件。我们还计算了光谱指数、香农熵和大脑网络的拓扑指数以及随机网络之间的相关性。相关性分析表明，虽然随机网络的谱和拓扑特性是完全独立的，但这些特征在脑网络中相互显着相关。此外，我们发现所研究的大脑网络的复杂性与同步性的稳定性成反比。总之，我们揭示了谱图理论方法可以可靠地应用于研究与状态相关的大脑网络同步性的稳定性。