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Open AccessArticle

The Maximum Eigenvalue of the Brain Functional Network Adjacency Matrix: Meaning and Application in Mental Fatigue Evaluation

1
College of Engineering, Zhejiang Normal University, 321004 Jinhua, China
2
Key Laboratory of High Efficiency and Clean Mechanical Manufacture, Ministry of Education of China, School of Mechanical Engineering, Shandong University, 250061 Jinan, China
*
Authors to whom correspondence should be addressed.
Brain Sci. 2020, 10(2), 92; https://doi.org/10.3390/brainsci10020092
Received: 6 January 2020 / Revised: 6 February 2020 / Accepted: 8 February 2020 / Published: 9 February 2020
(This article belongs to the Special Issue Advances in EEG/ MEG Source Imaging )
The maximum eigenvalue of the adjacency matrix (AM) has been supposed to contain rich information about the corresponding network. An experimental study focused on revealing the meaning and application of the maximum eigenvalue is missing. To this end, AM was constructed using mutual information (MI) to determine the functional connectivity with electroencephalogram (EEG) data recorded with a mental fatigue model, and then was converted into both binary and weighted brain functional network (BFN) and corresponding random networks (RNs). Both maximum eigenvalue and corresponding network characters in BFNs and RNs were considered to explore the changes during the formation of mental fatigue. The results indicated that large maximum eigenvalue means more edges in the corresponding network, along with a high degree and a short characteristic path length both in weighted and binary BFNs. Interestingly, the maximum eigenvalue of AM was always a little larger than that of the corresponding random matrix (RM), and had an obvious linearity with the sum of the AM elements, indicating that the maximum eigenvalue can be able to distinguish the network structures which have the same mean degree. What is more, the maximum eigenvalue, which increased with the deepening of mental fatigue, can become a good indicator for mental fatigue estimation.
Keywords: maximum eigenvalue; adjacency matrix; brain functional network; network characters; mental fatigue; electroencephalogram (EEG) maximum eigenvalue; adjacency matrix; brain functional network; network characters; mental fatigue; electroencephalogram (EEG)
MDPI and ACS Style

Li, G.; Jiang, Y.; Jiao, W.; Xu, W.; Huang, S.; Gao, Z.; Zhang, J.; Wang, C. The Maximum Eigenvalue of the Brain Functional Network Adjacency Matrix: Meaning and Application in Mental Fatigue Evaluation. Brain Sci. 2020, 10, 92.

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