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

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.

Mental Fatigue Has Great Impact on the Fractal Dimension of Brain Functional Network

“…Many researchers are dedicated to the studies of detection methods [ 2 ], neural mechanisms [ 3 ], and mitigation methods [ 4 ] of the mental fatigue, owing to the negative effects of mental fatigue on the human cognitive functions [ 5 ], especially serious in driving fatigue [ 6 ]. Recently, mental fatigue has been prevalently explored by the means of brain functional network with the neuroimaging technique of electroencephalogram (EEG) [ 7 – 9 ]. It has been widely proved that mental fatigue can lead to distinct changes in brain functional network structures, for example, the changes of small-world property [ 3 , 10 ].…”

“…Brain functional network, as one type of the complex networks in statistical physics, is a demonstration of the temporal correlations between different brain areas in the processes of neural physiological events [ 16 ]. It has become one of the most widely used techniques to investigate the neurodynamics of cognitive functions [ 17 – 20 ], which are especially sensitive to mental fatigue [ 3 , 9 ]. Since the small-world characteristic [ 21 ] and scale-free property [ 22 ] of complex networks were proposed, the studies of complex network topology have entered a high-speed developing period [ 23 ].…”

A quantum algorithm for solving eigenproblem of the Laplacian matrix of a fully connected weighted graph

“…Compared with its classical counterpart, our algorithm has a polynomial speedup on the number of vertices and an exponential speedup on the dimension of each vertex over its classical counterpart. In particular, our algorithm can also be used to solve eigen-problem of the weighted matrix, which is also of great significance [31][32][33][34]. We also show that our algorithm can be extended to solve the eigenproblem of symmetric (non-symmetric) normalized Laplacian matrix.…”

“…In addition, our algorithm can also extract the eigeninformation of W , which is of great significant [31][32][33][34]. See the detailed analysis in Appendix D.…”

High-order brain functional network for electroencephalography-based diagnosis of major depressive disorder

“…Brain functional network (BFN) constructed based on EEG has been widely used in the diagnosis of brain diseases ( Wang et al, 2015 ; Li et al, 2020 ). Since brain activity is dynamic in nature, some studies have shown that the dynamic change of FC over the whole scanning time may be the intrinsic feature of brain function ( Damaraju et al, 2014 ; Cohen and D’Esposito, 2016 ; Kudela et al, 2017 ).…”