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

Gang Li,Chengwu Wang,Weidong Jiao,Zhao Gao,Yonghua Jiang,Jianhua Zhang,Shan Huang,Wanxiu Xu

doi:10.3390/brainsci10020092

Gang Li, Chengwu Wang + Show 6 more

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https://doi.org/10.3390/brainsci10020092

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Journal: Brain sciences	Publication Date: Feb 9, 2020
Citations: 13	License type: CC BY 4.0

Affiliation: Zhejiang Normal University, Shandong University

Abstract

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.

Highlights

Brain functional network (BFN), as one type of the complex networks, is a demonstration of the temporal and topological correlations among different brain regions in the processes of brain neural activities [1]
We attempt to study the meaning of maximum eigenvalue in brain functional network (BFN) analysis and the application of the maximum eigenvalue in mental fatigue detection with the EEG data recorded with a mental fatigue model
Relationship thethe maximum eigenvalue and(Tthe sum ofResults the adjacency matrix (AM) for alpha1

Summary

Introduction

Brain functional network (BFN), as one type of the complex networks, is a demonstration of the temporal and topological correlations among different brain regions in the processes of brain neural activities [1]. It should ignore some technical details when constructing BFNs, such as the size, location, and shape of the network node, and the physical distance and geometric shapes of the connective edge. Explored BFN characters involve the degree, centrality, characteristic path length, clustering coefficient, and efficiency [7].

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