A Graph Theory-Based Modeling of Functional Brain Connectivity Based on EEG: A Systematic Review in the Context of Neuroergonomics

Graph theory analysis, a mathematical approach, has been applied in brain connectivity studies to explore the organization of network patterns. The computation of graph theory metrics enables the characterization of the stationary behavior of electroencephalogram (EEG) signals that cannot be explained by simple linear methods. The main purpose of this study was to systematically review the graph theory applications for mapping the functional connectivity of the EEG data in neuroergonomics. Moreover, this article proposes a pipeline for constructing an unweighted functional brain network from EEG data using both source and sensor methods. Out of 57 articles, our results show that graph theory metrics used to characterize EEG data have attracted increasing attention since 2006, with the highest frequency of publications in 2018. Most studies have focused on cognitive tasks in comparison with motor tasks. The mean phase coherence method, based on the “phase-locking value,” was the most frequently used functional estimation technique in the reviewed studies. Furthermore, the unweighted functional brain network has received substantially more attention in the literature than the weighted network. The global clustering coefficient and characteristic path length were the most prevalent metrics for differentiating between global integration and local segregation, and the small-worldness property emerged as a compelling metric for the characterization of information processing. This review provides insight into the use of graph theory metrics to model functional brain connectivity in the context of neuroergonomics research.


I. INTRODUCTION
The brain is the most complex organ in the human body, composed of 100 billion neurons connected by almost 150 trillion synapses [1], [2]. Over the last few decades, mapping of the human brain connectivity has gained considerable attention in the areas of neuroscience and cognitive neuroscience [3]- [7]. Modern network science, a mixture of dynamic systems theory, graph theory, and statistics, has been applied to the study of the functional and structural brain connectivity network under various states and conditions. Efforts have been made to study the topological properties of the brain for neurological disorder networks [8], brain disease and dysfunction networks [9]- [11], aging The associate editor coordinating the review of this manuscript and approving it for publication was Kang Li . networks [9], resting-state network [12], and high brain function networks such as perception, problem-solving, memory, and attention [13]- [16].
The graph theory approach, a powerful mathematical tool [17], graphically illustrates a complex network architecture based on the modern theory of networks. In 1736, the physicist Leonard Euler solved the problem of crossing the Pregel River, which is known as the ''Seven Bridges of Königsberg.'' The aim was to cross the seven bridges that connected two small islands in the Pregel River to the city of Königsberg only once and to return to the original location using an abstract representation and eliminating all features except for the landmasses and the bridges connecting them. In modern terms, Euler replaced each landmass with an abstract point (i.e., ''vertex'' or ''node'') and each bridge with an abstract connection (''edge'' or ''line''), resulting VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ TABLE 1. The classification of brain signals by frequency range with descriptions, psychological and behavioral conditions, and location in the brain.
in a mathematical structure called a ''graph'' or ''network.'' The contemplation of this problem led to the foundations of ''graph theory'' -the first true proof in the theory of networks. In 1741, Euler published his paper 'Solutio problematis ad geometriam situs pertinentis,' describing a hypothetical solution to the Konigsberg bridge problem [18]. Graph theory has since become a vital method in the field of electrical circuits and chemical structures. The modern era of graph theory began in the late 1990s with the discovery of small-worldness [19] and scale-free network models [20], enabling the quantification of brain connectivity patterns. Graph theory metrics are used to investigate the topological organization of the brain network and to characterize meaningful functional segregation and integration of the human brain.
The purpose of a systematic review is to identify, summarize, and analyze the findings of all relevant individual studies that address a predefined research question. The preferred reporting items for systematic reviews and meta-analyses (PRISMA) is a structured guideline to ensure reliable and meaningful review results. The protocol consists of 27 checklist items that help researchers to prepare and report evidence accurately and reliably, which in turn improves the quality of research [21]. The present study focuses on understanding the current state of knowledge regarding the applications of graph theory analysis in the context of neuroergonomics. Neuroergonomics, the study of the brain and behavior at work, applies methods and tools from neuroscience to elucidate neural signatures of human performance [22]- [24]. The brain possesses five different types of waves, and a variety of classifications of brain signals are available in the literature [25]- [27]. The most widely used taxonomy is based on the five frequencies of the brain waves measured in Hertz (Hz) as follows: delta (0.5−4 Hz), theta (4−8 Hz), alpha (8−13 Hz), beta (13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30), and gamma (30−150 Hz) [27]. Table 1 summarizes the information regarding the different types of brain signals according to their frequency ranges, with descriptions of the psychological and behavioral conditions [28]- [30].
The human brain is composed of four main parts: the cerebrum, cerebellum, brainstem, and diencephalon, which together control all bodily functions. Possessing the largest number of neurons, the cerebrum has four main lobes: the frontal, temporal, partial, and occipital lobes, each of which performs a specific function. The frontal lobe is associated with reasoning, movement, planning, emotion, and problemsolving. In contrast, the parietal lobe is associated with movement, recognition, and the perception of stimuli. The temporal lobe is associated with memory, speech, and the recognition of auditory stimuli, whereas the occipital lobe is related to visual responses [27], [29]- [35]. Information transfer among different brain regions reflects a combination of locally segregated and functionally integrated processes [36].
The ''connectome'' refers to the connectivity among different brain regions and the manner by which information is transferred among these regions [7], [37]. Three different types of connectivity are closely related: structural, functional, and effective connectivity [38], [39]. Structural connectivity encompasses the physical connections among neurons, known as ''neuroanatomical'' connections [40], which refers to the white matter connectivity in the brain. Functional connectivity is ''the statistical interdependencies between physiological time series recorded from different brain regions'' [41], [42]. Effective connectivity refers to the causal effect and the direct influence of one neural element on another [41], [43], [44]. Functional and effective connectivities are determined by sampling recorded signals over multiple time points, which provides a better understanding of brain function. For a review of functional and effective connectivity, we refer the reader to Friston et al. [41], Friston [42] and [45], and Goldenberg and Galván [46].
Continuous efforts in the neuroergonomics field have been devoted to studying the brain signals at work and in everyday settings [22], [23]. The number of useful analytical approaches used in neuroergonomics research is rapidly expanding; however, the functional brain connectivity and network topology in the context of neuroergonomics is largely unknown. Brain networks are typically modeled from data collected by different neuroimaging techniques. Modern electroencephalogram (EEG) systems are noninvasive, portable, wireless, and easy to use, rendering them attractive and applicable to neuroergonomics studies [47]. A considerable amount of work in functional connectivity studies has focused on the blood oxygenation level mainly by functional magnetic resonance imaging (fMRI) [3], [48], [49] due to its good spatial resolution. However, this technique has low temporal resolution and only provides an indirect measurement of brain activity. To study dynamic cognitive processes and the directional flow of information regarding brain activity, a high temporal resolution technique, such as EEG, enables capturing of the temporal dynamics of brain activity at the sub-second time scale [50], [51] and reflects the rapid changes in neuronal states [52]. Furthermore, EEG is capable of capturing the rich temporal information that aids identification of the directions of the flow of information among different brain regions (i.e., causal inference) [53].
Over the last two decades, EEG connectivity has gained considerable interest in clinical studies. The first application of graph theory to EEG data was reported by Stam et al. [54], who compared the functional brain network of control individuals and patients with Alzheimer's disease. However, little is known regarding healthy participants during everyday activity. Since the emergence of neuroergonomics, research attempting to characterize EEG data has been limited to the traditional analysis of EEG signals using individual electrodes, and the interdependencies among different EEG electrodes have been poorly addressed [55], [56].
Previous studies have succeeded in quantifying human states under a great variety of cognitive [57] and physical [58] tasks; nevertheless, further work is required to understand the dynamic temporal interactions among brain regions during everyday tasks. Accordingly, the current study sought to review patterns of brain connectivity using the computation of graph theory metrics in task-evoked EEG data.
In contrast to previous reviews [9], [44], we have restricted the current review to EEG studies that utilized the functional brain connectivity data in healthy participants relevant to the field of neuroergonomics. Furthermore, we summarized the pipeline for the construction of a functional network for EEG data. The primary focus of the current systematic review was to provide a framework that will facilitate the application of functional brain network analyses in the field of neuroergonomics in the near future. The present paper is organized as follows: Section II, Methods, presents the standards, search strategy, and eligibility criteria used for selection of the articles evaluated in the current review, as well as the extraction and synthesis of data and validity risk assessment; Section III, Theoretical Background, defines functional connectivity and the basic concepts of graph theory. This section also describes the pipeline for the construction of the functional brain network based on EEG data and discusses the different types of networks using a mathematical description of network measurements to characterize global and nodal brain connectivity; Section IV, Results, provides the results of the systematic literature search, the study characteristics, and a validity assessment of the considered studies; Section V, Discussion, discusses the applications of graph theory in cognitive functions and motor processing; and finally, Section VI, Limitations and Future Directions, outlines the current limitations and provides suggestions for future research.

A. REVIEW STANDARDS
This systematic review was conducted based on the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines [21], [59], [60]. Articles were selected based on several research questions, and the search strategy was designed to reduce the effect of research expectations on the current review. The Cochrane Collaboration method was used to minimize the risk of bias, according to Higgins et al. [61].

B. RESEARCH QUESTIONS (RQs)
•RQ1: With the advent of graph theory, what applications have been used to model human cognition and motor processing?
•RQ2: How can computational methods be used to characterize the underlying neural mechanisms of cognitive function and motor processing?
•RQ3: What does EEG add to the connectome? •RQ4: How can an undirected, unweighted functional brain network be modeled using EEG data?
•RQ5: Is the graph theory approach useful for characterizing the underlying neural mechanisms of human cognition and movement as measured by EEG in comparison with traditional approaches?
•RQ6: How can computational methods for modeling patterns of brain connectivity be implemented in neuroergonomics?

E. CRITERIA FOR INCLUSION AND EXCLUSION
Exclusion criteria were applied to limit the final selection of studies. To meet the eligibility requirements, we only included published articles that fulfilled the following criteria: (a) only English language publications; (b) experiments in humans; (c) studies using only the EEG technique; (d) experimental studies in healthy participants; and (e) content in peer-reviewed journals, conference publications, textbooks, and reference books. Articles with the following features were excluded: (a) studies on brain diseases or neural disorders; (b) studies that used neuroimaging techniques other than EEG; (c) experimental studies in infants; (d) studies on pathological conditions; and (e) studies that investigated only the restingtask state without considering task-evoked activity. These exclusion criteria were applied because completely different global topological properties and brain architectural features are obtained for these key factors. Accordingly, an additional 273 studies were excluded from the current review. During the screening phase, we identified a large number of studies that focused on the human brain network during resting-state tasks.
To collect all relevant articles in the literature search, the reference lists of the candidate articles (n = 325) were reviewed, yielding five additional articles that met the inclusion criteria. The findings of the literature search and the selection process are summarized in a PRISMA diagram (Fig. 1). This aspect of the study was performed from October 2019 to February 2020.

F. DATA COLLECTION AND SUMMARY MEASURES
Relevant information from the included articles was extracted; this information is summarized in Supplementary Material A, which displays the node definition, edge definition, graph theory metrics, number of participants, domain, experiment, and primary findings, providing answers to RQ1 and RQ2.

H. QUALITY ASSESSMENT
Study quality was independently assessed by two researchers (LI and WK). Any disagreement between the authors was resolved by consensus. The Cochrane Collaboration method [61] was used to assess the risk of bias in each experiment in the selected studies. The Cochrane Collaboration method has six main domains: (1) random sequence generation; (2) allocation concealment; (3) blinding of participants and personnel; (4) blinding to outcome assessment; (5) incomplete outcome data; and (6) selective reporting.
To assess the quality of the articles, the following judgments were used: low bias risk, unclear bias risk, or high bias risk.

III. THEORETICAL BACKGROUND A. FUNCTIONAL CONNECTIVITY
Functional connectivity measures the statistical interdependence of physiological time series recorded in different brain regions [62]. Functional connectivity has been employed by several studies due to it being the best choice for analyzing functional neuroimaging data and developing computer simulation models [63]. Since the calculations of functional connectivity are highly dependent on brain activities over the time series, a high temporal resolution technique such as EEG (< 1 ms) is the optimal choice to reflect the dynamic and rapid neural response [53]. Furthermore, EEG is a very promising method for connectivity analysis and causal inference, addressing RQ3. The statistical dependencies between pairs of regions are measured using different methods categorized into linear, nonlinear, and information-based techniques. These are sensitive to both linear and nonlinear statistical dependencies between two time series and can be used to assess causality. Table 2 provides an overview of the most established estimation methods for functional VOLUME 8, 2020  connectivity. It should be noted, however, that selecting the optimal estimation method is a challenging problem that is beyond the scope of this review article [64]- [66].
Univariate analysis should be used when analyzing the feature of a single signal from a particular neurophysiological technique, whereas multivariate analysis is typically applied when combining different neurophysiological techniques. A considerable body of evidence relies on linear methods; however, some researchers use nonlinear analysis methods to detect the nonlinear phenomena of the brain [78].
Other authors are opposed to using nonlinear methods since they are highly susceptible to noise [64].

B. THEORETICAL ASPECTS OF GRAPH THEORY ANALYSIS
Over the last two decades, the application of graph theory in the quantification of neurophysiological data has gained much attention in biology and neuroscience for the diagnosis of brain disorders such as epilepsy [79], [80], schizophrenia [12], Alzheimer's disease [62], rehabilitation after stroke [81], and other brain disorders (for a review, see Vecchio et al. [9] and Farahani et al. [3]). Several subsequent works aimed to study the topological configuration of the brain in response to task modulation. Most of the studies presented herein primarily focused on cognitive neuroscience; hence, one of the aims of the current review was to shed light on the functional connectivity of the brain at work and during everyday tasks.

C. APPROACHES TO GRAPH THEORY
For a better understanding of network properties, the data are presented as a graph (G), which is a basic topographical representation consisting of a collection of V vertices (nodes) that are connected by edges (E) (links or connectors) (Fig. 2), where G = (V, E). To study the human brain network on a macroscopic scale, the nodes represent brain regions (i.e., EEG electrodes/sensors), whereas the edges represent statistical measures of association, including anatomical, functional, or effective connections [5], [46]. Graph edges include weighted direct, unweighted direct, weighted indirect, and unweighted indirect. A direct edge shows that the information flows in one direction only and that one node's activity depends on the other (i.e., causal influence); however, an indirect graph shows that information flows in both directions along edges that connect. The weight of the line between two nodes reflects the connectivity strength of the edge, which allows for discrimination between strong and weak connections. Weak connections can be removed by thresholding.

1) PIPELINE STEPS FOR THE CONSTRUCTION OF A FUNCTIONAL BRAIN NETWORK BASED ON EEG DATA
The following eleven steps present the full pipeline for the construction of a functional brain network with graph theory of the EEG data using either the EEG sensor source method or space source method, which addresses RQ4. Previous studies have provided steps for either the sensor space method [40] or the source space method [53]. In the current study, we briefly describe the steps required for both methods focused on unweighted networks. We summarize all the steps of the pipeline, starting with the acquisition of EEG brain signals and ending with a statistical description of the brain network (Fig. 3). Our aim was to provide a simple stepwise method that can be used by non-expert researchers in the field.

a: DEFINE THE NODES OF THE BRAIN NETWORK
The nodes of the brain network represent the brain region. Defining the network nodes is a challenging step and significantly affects the outcome of the brain network analysis [83]. In EEG studies, nodes are defined using one of two approaches. The first approach is termed ''sensor signals'' or ''individual channel'' and relies on the predefined standard placement of the EEG electrodes ( Fig. 3a) [84]- [86].
While this approach is simple, the volume conduction, which is the leading cause of reduced spatial resolution, may affect the accuracy of the functional connectivity estimates [69]. Thus, a second approach based on EEG source space connectivity has been proposed [53], [87], which can be achieved by subdividing the brain into different regions and selecting the regions-of-interest based on a parcellation scheme and individually segregated anatomical regions-ofinterest (ROIs) from brain atlases [88], [89]. The source space is computed after the EEG signals are recorded (Fig. 3b), preprocessed, and epoched (Fig. 3c). The 3D electrode locations are then determined via the software acquisition system. To localize the brain source and reconstruct the time course, the inverse problem, which relies on dipole theory, must be solved [90], [91] by applying the following steps: (a) Obtain a head model by either using simple spherical head models or imaging a realistic head model by MRI (Fig. 3d). Realistic head models are usually preferable for an accurate calculation of the brain's electrical potentials and geometric characteristics; and (b) Estimate the source localization in the head model to determine the location of the dipole source and reconstruct the time course (Fig. 3e). Several algorithms are used for this purpose, including beamforming, low-resolution brain electromagnetic tomography (LORETA) [92], standardized LORETA (sLORETA) [93], exact LORETA (eLORETA), minimum norm estimate (MNE) [94], and weighted MNE (wMNE) algorithms. Subsequently, the source reconstructed time series is partitioned into individual ROIs from the brain ( Fig. 3f) determined from functional atlases [95] to obtain a regional time series (Fig. 3g).

b: PREPROCESS THE EEG DATA
After high-quality EEG signals are recorded from the scalp surface, the continuous EEG time series data (Fig. 3b) must be preprocessed for segmentation, filtration, denoising, and artifact removal (Fig. 3c) [96]. EEG data are contaminated by different types of artifacts, which are categorized as physiological or non-physiological [97]- [100]. Various methods for data cleaning are discussed in [34], [101]. Then, specific time windows are extracted from the cleaned continuous EEG data ''epochs.''

c: DEFINE THE EDGES
The edges represent connections between different neurons or brain regions and exhibit various patterns of connectivity, including structural, functional, and effective connectivity [102]. In functional connectivity, the edges represent the time series correlation between two different nodes ( Fig. 3c) or regions (Fig. 3g). The edge is categorized as either direct or indirect with or without weights. Weights provide more information about the relationship between node pairs.

d: COMPUTE THE CONNECTIVITY MATRIX (A)
The connectivity matrix is known as the adjacency matrix and contains information regarding the associations among connectivity patterns. The connectivity is described by an N × N symmetric matrix, in which the rows (i) and columns (j) denote nodes, and matrix entries (aij) denote edges. There are two types of metrics: one is based on channels (Fig. 3i) and the other is based on the brain region (current densities for each brain region pair) (Fig. 3h).

e: CONVERT THE CONNECTIVITY MATRIX INTO A BINARIZED MATRIX
Matrix binarization is performed to convert the adjacent matrix to an unweighted matrix (Fig. 3j). For matrix binarization, a threshold value is calculated for each element. If the correlation measures for each pair exceed the threshold, value edges are added between node pairs (otherwise no edge exists) [37].

f: CHOOSE A THRESHOLD VALUE
The optimal threshold value is an open question in the literature. Thresholding helps to simplify the complexity of the brain network calculations by eliminating weak, noisy, and insignificant edges from the network. Moreover, thresholding facilitates the definition of the null model for statistical comparison [4], [40], [80]. Selection of the threshold value significantly affects the network topology properties and the ability to detect differences among groups, ages, and genders. Selecting an inappropriate threshold method creates instability and increases the bias; therefore, careful selection is crucial. A key factor is to select a method capable of controlling and minimizing the occurrence of type I errors (i.e., false-positives) [103].
Some criteria for appropriate threshold selection are reported in [103]- [105]. A variety of thresholding methods are available, including fixed threshold, fixed average degree, and fixed edge density (for a detailed review, see [104], [106]). However, none of these methods are free from bias. To perform statistical inference on connectome data, some researchers have suggested to ''independently test the hypothesis of interest at each discrete density along the curve'' [107]. In contrast, others have recommended more sophisticated methods, such as false discovery rate (FDR) error metric, network-based statistics (NBS) [88], and subnetwork-based analysis [88], [108], [109]. The threshold-free network-based method provides statistically significant thresholding values [108]. Drakesmith [110] proposed a multi-threshold permutation correction approach for improving sensitivity to substantial group effects with minimal a priori assumptions. The minimum spanning tree avoids methodological biases when comparing networks [111] and helps to rectify thresholding issues [112]. A novel methodology, namely the minimum connected component (MCC), has been proposed by Vijayalakshmi et al. [113], which overcomes the threshold issues.

g: ESTIMATE THE FUNCTIONAL CONNECTIVITY MEASUREMENT
A comparison between the methods for functional connectivity estimates are summarized in Table 2. A comprehensive review of these articles is provided in [44], [114]. Unfortunately, there is no optimal method to universally assess the functional connectivity [115], [116].
In general, the EEG signals are best expressed based on frequency domain characteristics to distinguish between neural and artifact signals; thus, methods for frequency-based functional estimators are particularly attractive [119]. Furthermore, the extraction of several different frequencies of brain signals is possible with the frequency domain method. Pereda et al. [78] support the use of multivariate analysis methods, but nonlinear methods have also been used since they are more sensitive to the detection of nonlinear coupling in EEG signals [116], [120], [121]. Several MATLAB-based toolboxes are available for estimating the source or functional connectivity and analyzing the network measurements, as summarized in [53].

h: CONSTRUCT THE NETWORK
Mathematically, a network is a matrix [9], and the binarized matrix is converted into a sparsely connected graph, represented as a scalp graph (Fig. 3k) or cortex network (Fig. 3l).
i: ANALYZE THE DATA USING GRAPH THEORY Different graph theory metrics are used to quantify network structures by analyzing the topological properties of the network (Fig. 3m). Graph theory is used to extract features from the functional connectivity network. Different toolkits have been developed to visualize and analyze topological properties, as summarized by Xia et al. [122] and Hassan and Wendling [53]. In the following section, we present a detailed description of the measures used to detect aspects of functional integration and segregation for unweighted networks.

j: APPLY STATISTICS
Statistical methods are applied to compare graph theory metrics and topological network properties and assess their statistical significance (Fig. 3n). This step is usually performed by either comparing two different states (alert vs. drowsy), conditions (movement vs. rest), populations (healthy vs. diseased), or genders (males vs. females) or by comparing results with a theoretical reference network [128]. Meanwhile, there is no predefined way to assess the statistical variability. The application of confidence intervals is essential for measuring the significance of the obtained results and proving the reliability of graph analysis of functional brain networks. Other methods for statistical inference include nonparametric statistics, permutational statistics, and bootstrapping, which are the most appropriate for the nature of EEG data [2]. The aforementioned statistical methods failed to address the graph topology between the massive edge features, leading researchers to develop a novel pathway for investigating the phenotype of connectome features [82]. An automatic k-partite graph detection (KPGD) algorithm succeeded in identifying the k-partite subgraphs in complex networks [124]. Hierarchical Bayesian Gaussian graphical models have been recently proposed to provide robust brain network estimation [125], [126].

k: CLASSIFY THE CONDITIONS
Several methods have been employed to classify different brain states (Fig. 3O). Functional connectivity estimates have been used to classify fatigue and non-fatigue conditions [127], whereas hand movements have been classified based on network node strength [128]. Other classification algorithms, such as artificial neural networks [129] and support vector machines [130], [131], have been used to classify mental workload and mental fatigue with connectivity features.

D. GRAPH THEORY MEASURES AND NETWORK TOPOLOGY PROPERTIES
Network measures are calculated for the quantitative investigation of network properties. Table 3 presents a short nonmathematical description of the commonly used network measures categorized into global (graph) and local (nodal) measures. Global measures include the characteristic path length (PL), clustering coefficient (CC), small-worldness (σ ), global efficiency (Eglobal), local efficiency (Elocal), transitivity (T), network density, assortativity (r), and modularity (Q); whereas, nodal measures include nodal centrality, node degree, hubs, degree distribution, degree correlation, betweenness, eigenvalue centrality, eccentricity centrality, closeness centrality, nodal efficiency, and motifs. The provided definitions are limited to unweighted graphs. Detailed descriptions of these network measures and their interpretations are provided in several studies [4], [132]- [135]. Furthermore, reviews on the application of graph theory in neuroscience can be found in many previous works [102], [136], [137]. Several software packages are available for the identification and characterization of network measurements, including BCT [5], EEG-Net [138], [139], and BrainNet Viewer [122].

1) NETWORK TYPES
There are four types of networks: regular, well-ordered, or lattice-like networks; random networks; small-world networks; and scale-free networks (Fig. 4) [140]. These different networks are distinguished based on the number of local segregation events (represented through CC) and the global integration between nodes (represented through PL). Regular networks have a high CC and a long PL, indicating that the network is robust but inefficient at transferring information. In contrast, random networks have a small CC and a short PL, indicating that the network is efficient at transferring information but is not robust.
A small-world network is intermediate between regular and random networks and has a short PL similar to a random network, and a higher CC than a regular network [141]. Small-world networks are considered near-optimal networks in terms of segregation, integration, cost, and performance [62], [74]. A scale-free network is unique due to its extremely short path length [136], [158], [159], and strikes a balance between global and local communications [160] with a power-law degree distribution. Other network classifications have been proposed by Kaiser [102], which are based on topological and spatial organization.

A. STUDY CHARACTERISTICS
A total of 57 articles met the selection criteria. Just under half of the selected articles (44%; n = 25) were published from 2006 to 2016, whereas over half were published within the last three years (56%; n = 32). Thus, this review demonstrates an increasing trend in brain function studies using brain connectivity techniques and graph theory metrics (Fig. 5). We expect the number of future studies to increase dramatically over the next several years. VOLUME 8, 2020

B. QUALITY ASSESSMENT
To evaluate the strength of evidence in these studies, we applied the standards of the Agency for Healthcare Research and Quality [161]. Studies of good quality were judged to have a low risk of bias; studies of fair quality were judged to have two unclear criteria; and studies of low quality were judged to have a high risk of bias. The overall quality of the studies was categorized as good, fair, or low if the number of low-risk domains was ≥ 4, = 3, or ≤ 2, respectively.
Of the 57 studies included in this systematic review, n = 18 were classified as good-quality, n = 7 were classified as fair-quality, and n = 32 were classified as low-quality (Fig. 6).
This finding can be attributed to the fact that most studies neglect to describe random sequence generation and allocation concealment. Moreover, an unclear bias results from unclear selective reporting of the data and attrition; thus, the level of evidence in the included studies is low.
The present review analyzed the performance in different domains and found that the majority of the reviewed articles focused on fatigue followed by workload assessment.
Overall, the evidence indicates that cognitive functions (80%) are more frequently addressed than motor processing (20%). Techniques for estimating functional connectivity, including PLV [71], PDC [77], and PLI, exhibited the greatest potential impact (40%) (Fig. 7). Numerous studies (n = 9) employed the PLV technique since it overcomes the limitations involved in using traditional coherence methods and calculates the linear correlation among EEG signals [71]. The PLV technique is followed by PDC in frequency of use, since this technique allows assessment of the statistical interdependence of EEG signals in the frequency domain [77], [162]. Further, Stam et al. [62] suggested the use of PLI for non-stationary EEG data. PLI is less sensitive to volume conduction than other connectivity measures [72], [163], and has a lower impact on gaitphase-locked artifacts [164]. The use of a weighted network leads to a rich topological brain organization; however, many of the selected studies (n = 48) used an unweighted network, known as a ''binarized network,'' whereas only a few (n = 9) applied a weighted network. The CC and PL are the most frequently used graph theory metrics (average, normalized, or weighted) (n = 33 and 26, respectively) (Fig. 8). We further found that approximately 79% of studies analyzed indirect networks, while 21% assessed direct networks. Our findings are consistent with the FMRI study reported by Bullmore and Sporns [4]. Both the CC and PL are helpful in the evaluation of small-world organization [156]. The CC is useful for quantifying functional segregation in the brain, whereas the PL is useful for quantifying network integration. Furthermore, the calculation of both Eglobal and Elocal depends on these two metrics. The construction of the connectivity matrix and calculations of the matrices can be accomplished with the aid of different software programs. A commonly used toolbox in the selected articles (n = 22) is BCT [5], which has a large number of topological metrics and is an open-source MATLAB toolbox.
A critical aspect of any EEG functional connectivity network is the selection of the number of nodes, which are represented by the recording electrode channel number. Two recommendations for this selection were found in the literature. A denser electrode distribution results in a high clustering coefficient and may cover more areas for future findings. A large number of electrodes (i.e., ≥ 64 channels) is recommended for the EEG source connectivity method [53], [147], [165], [166].
Furthermore, a large number of electrodes increases the accuracy of electrical source estimation [167] and signal preprocessing [47]. In contrast, García-Prieto et al. [168], Li et al. [169], and Wang et al. [170] recommend fewer than 32 electrodes, demonstrating that a small number is adequate to cover the ROI and obtain reliable information. A small number is also suggested by Luck [33], indicating that the use of 16-32 active electrodes is better for monitoring brain activity. The electrode numbers used in previous publications are summarized in Table 4. According to our analysis, 20 studies followed the first recommended condition, with ≥ 64 electrodes, 31 studies followed the second strategy (≤ 32 electrodes), and the remaining studies (n = 6) used between 32 and 64 channels.
The demographic distribution of the studies included healthy male and female participants (Fig. 9). Of these, 21 studies used males only, whereas none of the studies used only females. The majority of studies had a higher number of males than females (n = 16). The remaining studies (n = 9) did not precisely describe the number of participants by gender, as presented by the green bars (Fig. 9).

V. DISCUSSION
This section describes the major findings of the reviewed studies. Considerable changes in the functional brain network configuration have been demonstrated in different cognitive and physical states. This section also provides insight into L. E. Ismail, W. Karwowski: Graph Theory-Based Modeling of Functional Brain Connectivity Based on EEG   the application of graph theory in the study of cognitive and motor processing, in line with RQ1, RQ2, and RQ5.
Application of Graph Theory in Functional Brain Network Analysis: This subsection is grouped into six main domains: fatigue, workload, working memory, exertion, perception, and motor processing. There is some degree of overlap in the cognitive processes. For instance, the cognitive workload is directly related to the allocation of resources to the working memory and its association with attentional processes, which can be substantially affected by mental fatigue [171].

A. CONNECTIVITY STUDIES ON FATIGUE
Mental fatigue is a complex psychobiological state in which a high level of cognitive and motor activity is required during a prolonged task [172]- [174]. In general, fatigue diminishes human performance by slowing the response time, increasing the error rate, increasing drowsiness, and causing musculoskeletal disorders. Previous studies have addressed the underlying neural mechanism of mental fatigue in realistic applications [175]. In particular, the effect of mental fatigue on vehicle driving and piloting performance has gained much attention in the neuroergonomics literature [172], [174]- [180]. The PSDs of the alpha and theta bands have been shown to  be robust indices of neural changes related to fatigue [175], [181]- [197]. A significant increase in PSD for both frequency bands is primarily associated with mental fatigue in the frontal cortex, medial prefrontal cortex, frontocentral, occipital, and parietal brain regions [181]- [183], [185]- [187], [191], [195], [196], [198], [199]. Recent studies in cognitive neuroscience have explored the interactions among brain regions after the performance of fatiguing tasks. The functional connectivity of the frontal, central, and parietal brain is strongly correlated with mental fatigue [200]. The middle frontal gyrus and several motor areas are connected during tasks that require sustained attention [131]. Different patterns of connectivity between the right and left hemispheres in sensorimotor areas have also been demonstrated during a state of fatigue [201], similar to the findings of Liu et al. [200] in different brain regions.
In addition, some studies have observed denser functional connectivity during post-fatigued tasks in comparison with pre-fatigued tasks, indicating that the human brain exhibits stronger coupling during fatigue to maintain information transmission until the required task is accomplished [56], [202]- [206]. A higher phase coherence for the alpha and theta bands [205] and a higher PLI for the delta band [206] have been demonstrated during drowsiness in comparison with a state of alertness, indicating a lower degree of asymmetry in the phase difference.
However, there are also contradictions in the literature; for example, it has been reported that the functional connectivity of the alpha band in the parietal-to-frontal region [200] and of the alpha and beta bands in the frontal-to-parietal region [130] become weaker as mental fatigue increases. Furthermore, it has been shown that fronto-occipital coherence values in the alpha range decrease during the shift from alertness to drowsiness [207]. Results of the aforementioned studies support the notion that cortical-to-cortical functional couplingmainly in the frontal, central, and parietal lobes of the cerebral cortex-can characterize the brain during mental fatigue over short time scales.
Changes in the topological properties of the brain network reflect human mental states. For instance, an increase in the maximum eigenvalue of the alpha band reflects a deterioration of performance in humans [208]. Poor attention during a mental task is characterized by a decreased PL in the delta and theta bands [209] and an increased CC [169], [210], [211]. The results reveal that fatigue increases Elocal but reduces Eglobal, indicating that the resources of the brain may be reorganized and the interactions between regions may be inhibited. This trend reflects a decrease in the ability of the human brain to integrate information during fatigue [209] and leads to a small-world configuration [169], [204], [210]. A lack of awareness as a result of mental fatigue has been demonstrated by an increase in the CC and in the Eglobal value of the sub-band (36)(37)(38)(39)(40)(41)(42)(43)(44) [212].
An increase in the degree of centrality in the right parietal brain regio in the delta rhythm [170], [202], and in all frequency bands [56], [208] indicates good connectivity among nodes with a reduction in alertness. However, contrasting results have also been demonstrated, such as an increase in the percentage of unconnected nodes, indicating breakdowns in connections during the shift from alertness to drowsiness [209]. Moreover, some studies have reported decreases in the CC, average degree, and network density, and an increase in the PL after a fatiguing task [130], [132], [201], [213], [214].
An increase in the betweenness centrality in the frontal cortex has also been observed during fatigue [132]. A midtask break (rest) is an effective way to improve the efficiency of the brain network, thereby mitigating the occurrence of fatigue [132], [215], as evidenced by a slight increase in both the CC and PL after a rest between sessions.
Since human performance declines over time, a positive correlation between the time spent on a task and network metrics (primarily the node degree, CC, and PL) has been observed [170], [213]. However, the results of some studies contradict these findings [15], [127], [131], where an increased time spent on a task results in a linear reduction in the network topology. An increased PL and a decreased small-worldness result in a less optimal brain network as the time spent on tasks increases [127]. Furthermore, a prolonged time spent on tasks reduces the network betweenness in the central and left frontal regions but increases the network betweenness in the right parietal region.

B. CONNECTIVITY STUDIES OF MENTAL WORKLOAD
As discussed by Young et al. [216], the mental workload is one of the most widely invoked concepts in the field of ergonomics [217]- [220], and as a multidimensional construct, can be defined in terms of the resources available to meet task demands [221]- [231]. The mental workload assessment based on neuronal data has been of great interest in neuroergonomics studies (for a review, see Borghini et al. [172]). The neuro-indices of cognitive workload [232], including EEG-based workload, have been discussed in the context of human-computer interactions [233] and a virtual driving environment [234].
The PSDs of the frontal theta, occipital theta, and parietal alpha have been demonstrated as a powerful assessment tool for discriminating the state of mental workload. A reduced parietal alpha PSD and an increased frontal theta PSD have been observed as task difficulty increases [172], [177], [235]- [248]; however, other studies have shown inconsistent results [249].
Discrimination between different levels of difficulty is reflected in the functional connectivity of the brain network, mainly in the prefrontal and parieto-occipital regions. Furthermore, a decrease in functional connectivity has been shown to indicate a reduction in human accuracy during difficult tasks [250]. A lower PLV has been demonstrated in parieto-occipital regions during highly difficult tasks in comparison with tasks of lower difficulty levels [251]. The weighted PLI value for the alpha band in all brain regions has been shown to decrease under a high cognitive workload, whereas an increase is evident in the coupling of the theta band during a physical task [252]. Dimitrakopoulos et al. [87] found that the majority of changes related to the difficulty of cognitive tasks occur in frontal theta and beta activity, based on the features obtained from analysis of functional connectivity. VOLUME 8, 2020 Discrimination between cognitive difficulty levels and the detection of cognitive impairment [113] can be performed by analyzing graph measurements [253]. Patterns vary between high and low cognitive or physical workloads. Furthermore, results may vary from the left to the right hemisphere [254]. The significance of these classifications can help to characterize dangerous situations in the workplace [255].
The Eglobal and Elocal values have a significant impact on workload level, where increases in the alpha and beta Elocal activities are associated with elevated workload levels. The Eglobal beta pattern shows a unique trend [256]. Huang et al. [257] observed a decrease in the Elocal of the theta band and an increase in the Elocal of the beta band during play. Furthermore, a lower Eglobal in the beta band and a higher Eglobal in the theta band were observed when comparing the network organization with that of the resting state. During the transition from subitizing to retrieval during a mathematical processing task, an increase in the Elocal and Eglobal values was observed for the delta, theta, and alpha bands, mainly in the fronto-parietal regions [253]. Particularly, increased effort results in an increased Eglobal, yielding a more integrated network and a higher transfer rate of parallel information. A reduction in the segregation process is reflected by a reduction in the CC and modularity. Zhang et al. [258] reported less modularity, less clustering, a high Eglobal, a low Elocal, and a greater physical synchronization distance in the beta and lower gamma bands during difficult mental tasks. Moreover, a reduction in the alpha and beta CC, with a significant increase in the alpha strength in the central and parietal brain, has been demonstrated for high workload levels [129], [259]. These results demonstrate that during a high workload, the human brain network has a small-world network topology (less clustered and more globally efficient) [260], [261]. Interestingly, Klados et al. [253] observed that an optimal small-world organization is evident during both mathematical tasks and rest. Vijayalakshmi et al. [113] demonstrated a high degree of interactions among different electrodes and increased functional brain segregation of the beta bands [14].
Local properties appear to be more crucial than global properties during cognitive processing. For instance, the local CC is much greater than the global CC during a target recognition task [262]. Moreover, the node strength exhibits a higher value in the frontal lobe and left hemisphere than that in global activity [253]. Furthermore, Enodal increases in motor executive areas during finger-tapping tasks [263].

C. CONNECTIVITY STUDIES OF WORKING MEMORY
Working memory is related to the process of storing and processing information. Many situations in the workplace require the manipulation and recall of information for decision-making and problem-solving. The ability to recall and store information is negatively impacted by fatigue, stress, and workload, which in turn affects attention levels, situational awareness, and learning performance. Training, practicing, and learning reduce the workload on short-term memory by storing necessary information in long-term memory. Thus, cognitive brain function can be improved through working memory training, as evidenced in topological network changes, mainly in the beta band. An inverted U-shaped curve is observed for the CC and small-worldness, whereas the PL exhibits a contradictory pattern [160]. Taya et al. demonstrated that the global network properties for the high-frequency bands increase during training, whereas the local properties and small-worldness reduce [13]. Interestingly, the node betweenness exhibits a change in the frontal and temporal regions during training. However, Langer et al. [264] found an increase in the theta CC and a reduction in the theta PL length during training-induced working memory. Therefore, training improves the local network connectedness and global efficiency of transferred information.
A greater phase coherence of the theta band in the frontal and posterior parietal regions is evident when comparing a well-trained, memorized sequence experiment with a novel task [242]. The brain organization of well-educated participants is less organized than that of less-educated participants during a working memory task [265]. Furthermore, a large scale network reconfiguration was found in the coherence theta band after training [264]. Although the connectome approach has been applied in limited studies to understand the brain organization underlying cognitive training, the approach is very promising for the characterization of cognitive functions.
Studies on working memory have primarily focused on the functional interaction between alpha and theta bands in the parietal, frontal, and parieto-occipital brain regions. Klimesch [266] reported that a long-term memory leads to desynchronization of the alpha band, whereas a short-term memory leads to synchronization in the theta band. Changes in phase synchrony of the theta and alpha bands in the frontal and parieto-occipital regions were found with different workload memory levels [267].
Different topological properties have been observed in all frequency bands during encoding, storage, and retravel [268]. Working memory tasks require a high degree of cognitive effort, resulting in lower clustering and modular configurations but a higher Eglobal for the alpha, beta, and gamma bands [269]. When comparing a working memory task with a resting task, a high degree of functional integration in the theta band [250] and low functional segregation in the alpha band have been observed [16]. Thus, a small-world topology is evident with respect to the storage and retrieval of memories in all frequency bands [268].

D. CONNECTIVITY STUDIES OF MOTION
Motion is essential for everyday tasks since ''human action is orchestrated by mind (and brain) and body interactions'' [270]. The contralateral somatosensory, ipsilateral somatosensory, and motor areas of the brain are strongly related to the function of motor processing. Before movement occurs, there is a transfer of information from the contra-to the ipsilateral hemispheres, whereas the opposite pattern occurs after movement [76]. The increase in network edges during the preparation for movement demonstrates the need for a higher degree of information exchange in order to execute movement-related tasks [147]. Moreover, decreased accessibility and increased centrality have been observed during the preparation and execution of finger movement tasks.
Different patterns of coupling are observed for different intervention strategies. Particularly, different intensity levels during a cycling task generate different patterns of brain connectivity in the alpha and beta bands of the prefrontal motor and central areas [271]. Furthermore, an increase in synchronization has been observed in the parietal and occipital lobes after physically and visually fatiguing tasks [203]. Increased mutual information values for the beta band have been observed during a finger-tapping task, reflecting an increase in the flow of information [263]. Lastly, a strong interaction between the sensorimotor and prefrontal areas has been shown to occur during the transition period from the resting state to the hand movement [272].
Local network properties have been considered during leftand right-hand movement tasks in order to classify different movements [273]. Ghosh et al. [128] showed that the node strength could be applied to the classification of hand movements without the need for a classifier. The Enodal value for the left sensory and bilateral primary motor cortices increases during motion-related tasks but decreases in posterior parietal areas [263]. Furthermore, researchers have observed an increase in the functional connectivity of the motor region during arm movements, as well as reduced node accessibility and increased node centrality [274], [275]. Two years later, the same research group [276] found that arm movements significantly reduced network connectivity, primarily in the alpha and beta bands, and reduced the weighted PL only during movement of the left arm. However, neither the CC nor the small-worldness exhibited any significant changes. Jin et al. [263] observed the economy of small-worldness in alpha and beta band networks during finger movement and resting tasks. The medial premotor and bilateral prefrontal cortex for the gamma and beta bands appear to have greater connectivity and a higher CC, but a shorter PL during motor tasks [105]. Significant changes in the hubs of the lower beta and gamma bands in the superior parietal somatosensory cortex have been shown to characterize visuomotor associations [277]. A comparison between the node degree of spectral coherence and that of imaginary coherence in the beta band during a motor task showed that the spectral coherence network outperforms the imaginary coherence network in the contralateral motor cortex [278].

E. CONNECTIVITY STUDIES OF PHYSICAL EXERTION
Exertion is directly related to workload [279] and reflects the fatigue, strain, intensity of effort, and discomfort that a subject may face during physical exercise [280]. An increase in partial theta coherence has been observed in the frontal region during working memory tasks associated with physical exertion. An interesting U-shaped pattern was initially observed in the CC, where the CC of the theta band increased during both physical exertion tasks and mental tasks and decreased significantly when the tasks became more difficult [250]. The study limited its investigation to the frontal brain region; however, future studies should investigate the topological properties across the entire brain. A bilateral connectivity pattern of information flow during different exertion levels was observed by Comani et al. [271]. A recent study addressed the functional brain patterns and network topology during a cycling task [281]. Three graph theory measures were computed in EEG source level for six different difficulties. The local efficiency remained constant in both the alpha and beta bands, indicating that fatigue did not alter the segregation of the brain network. The alpha global efficiency is significantly changed between pre-and post-cycling due to the great requirement for alertness. However, the density of the network is decreased in the beta band during the high endurance stage, demonstrating the influence of the decisionmaking process.

F. CONNECTIVITY STUDIES OF PERCEPTION
The study of perception requires comparisons between several cognitive functions (e.g., attention, consciousness, and memory) and the duration of the task. One study reported significant changes in the theta band phase-synchronized coupling in the fronto-parietal area during a target recognition task [262]. Furthermore, low modularity, high clustering, and strong interactions among node hubs are evident during the cognitive processing of targets. The time spent on a task directly affects the emotions, mood, arousal state, and cognitive load of participants [282]. Ghaderi et al. [143] studied nonlinear differences in the brain during a time-perception task. Two groups of participants-those that overestimated the time and those that underestimated the time-exhibited significant differences in the beta CC. Furthermore, a higher perception of task effort revealed strong beta coherence coupling in the prefrontal-motor area [271]. The global efficiency, transitivity, and degree in the overestimation group were lower than those in the underestimation group.

VI. LIMITATIONS AND FUTURE DIRECTIONS
The results of the present study reveal the growing interest in the investigation of brain connectivity with respect to the execution of specific tasks. The presented review also demonstrates that the use of graph theory metrics with EEG data yields reliable and feasible results; however, many challenges must be overcome for further progress. The application of graph theory metrics in neuroergonomics will help scientists to study connectivity patterns during everyday activities, and may provide more rich information regarding brain activity in comparison with single-channel features in everyday settings [253]. Therefore, future work should focus on the use of graph analysis measurements for different real-world applications. The studies discussed in the current review lack designs with ecological validity. The studies on fatigue and VOLUME 8, 2020 workload tasks were conducted in well-controlled simulated environments (i.e., driving and piloting). Motion tasks were limited to finger movements such as tapping, and exertion tasks were limited to cycling activity [250]. The study of perception has been limited to the classical oddball experiment [262]. Regularly performed tasks in everyday settings such as handling, lifting, gripping, grasping, pulling, pushing, assembling, sorting, manual inspection, and lower limb movements have not been well quantified using graph theory metrics. Therefore, new exploratory studies are required to address real-world applications.
The superior temporal resolution of EEG helps to capture the rapid and dynamic changes in brain activity. Few studies have considered the flow direction of neural information. These studies have used the Granger causality, DTF, PDC, and generalized PDC to quantify the strength of the interaction and causality between two signals. These methods predict the future of signal X from the past of signal Y and vice versa. The frequency-domain method is more commonly recommended for EEG due to its ability to extract neural changes at different frequency bands [44].
Methodological choices through EEG recording, preprocessing, and analysis significantly impact the functional connectivity estimations and network topology. These include the choice of reference, the presence of artifacts, the confounding effect of volume conduction in EEG (in signal space), and the inverse problem (in source space). Hence, future research should explore the effects of different types of references on the connectivity measurements, as discussed in [118], [283]. To mitigate the volume conduction effect, less sensitive connectivity estimators to volume should be used [72], [76], [163]. Other works offer additional suggestions for reducing the effect of volume conduction, such as using spatial filters (Laplacian montage), applying current source density through the Surface Laplacian, and implementing the source space method [53], [65], [284]. Despite the application of source space methods, there is no unique method to solve the inverse problem without assumptions and limitations. Additionally, the source space method is difficult to implement, and the effect of volume conduction can never be completely abolished [165]. Overall, ''none of the proposed methods have been shown to completely overcome the limitations of the volume conduction or the field spread problems,'' as mentioned by Hassan and Wendling [53].
Several studies have focused on analyzing the static functional connectivity of EEG data. The human brain is a complex system with dynamic behavior over time. An extension, known as the dynamic brain network, has been applied to track the spatiotemporal dynamics of functional brain networks. It is based on the use of the EEG source connectivity combined with a sliding window approach [285]. Changes to reconfigurations of connectivity patterns over time have been observed in task-based [286] and even in resting state [287] studies. There is a continuous reorganization of the human brain network in response to internal and external stimuli. Novel insight into the neural mechanism has been provided in emotional-based studies [288] and mental imagery [289]; therefore, there is potential for considering the dynamic analysis of functional brain networks in future studies.
An emerging method for the estimation and classification of the dynamic functional brain states is to apply clustering-based analysis, especially the k-means [290] from the windowed covariance matrices. Allen et al. [291] proposed a data-driven method to assess the dynamic functional connectivity patterns of the whole brain based on spatial independent component analysis, sliding time window correlation and k-means clustering of windowed correlation matrices. The results improved the understanding of neural shifts occurring during mental work. Other studies have applied k-means clustering to identify the functional connectivity patterns that reoccur over time and across subjects [292]- [294]. However, the method requires the setting of initial values and the number of states to achieve a good performance [295].
Many attempts have been made to minimize muscular and ocular artifacts in EEG data [296]- [299]. None of the developed methods guarantee artifact-free data. It is unknown to what extent the reduction of artifacts could influence the connectivity measurements. Filtering is used to avoid antialiasing and to eliminate the effect of direct current. However, careful selection of filtering is crucial since filtering affects the phase and amplitude of EEG signals; thus, a zero-phase filter is highly recommended.
Functional connectivity patterns and graph theory have proven to be powerful tools for the characterization of brain signals. However, the ability to use these measurements as an input parameter for developing predictive models, adaptive systems, or monitoring systems has been poorly addressed [130], [255], [300]. One of the most challenging goals in the field of neuroergonomics has been to develop smart systems that can accurately monitor and detect an operator's mental state and the intention of movements at work [129], which addresses RQ6. Another challenge in implementing graph theory is the attraction model of smallworldness, which has been used to characterize fatigue [170], [204], [210] and motion [263], [274]. As the primary features, a high CC and short PL provide a more integrated and less segregated network organization; however, the methods used to evaluate this model have some constraints that should be considered in the future [301].
Brain connectivity studies require high dimensionality statistical analysis methods that consider the multivariate connectivity edges to obtain accurate estimates of model parameters. A challenging area of research is the application of advanced statistical models in tasked-based EEG functional brain networks [43].
Further research is needed to avoid the arbitrary selection of the threshold value in a binary network to minimize bias. Recently, the application of the minimum spanning tree results has minimized the bias observed from thresholding [206]. The chance of having a network with a high false-negative value and threshold bias motivated researchers to propose novel computational methods [110], while others implemented a weighted network since it is more informative [44]. In that case, care must be taken because variation in weight affects the network topology [107]. The unweighted network still dominates the literature since it simplifies the complexity of brain signals by eliminating the weakest connections [275]. Although several thresholding approaches have been proposed, there is no reliable method that efficiently filters brain information [113].
There exists some controversy regarding the adequate number of electrodes and the effect of the electrode number on connectivity patterns [165]. A considerable number of studies have used large numbers of electrodes [275]. Finally, the CC and PL have proven to be crucial metrics for defining functional integration and functional segregation. More attention is needed in regard to other network metrics, such as the maximum eigenvalue [208] and motifs [259].
Nodes and edges are the basic elements for the construction of a network, and their selections significantly affect the network property estimations [306]. Complex networks composed of a large number of nodes and edges require advanced methods to decompose the graph into a nested hierarchy of increasingly cohesive subgraphs [307]. Those include k-core [308], k-truss [307], and k-core-truss [309]. Furthermore, complex structures of the brain network have complex interactions between nodes and a large number of edges. Therefore advanced methods have been developed to determine the hierarchal network structures, including the Kernighan-Lin Algorithm, Spectral Bisection Method, Divisive Algorithms, Agglomerative Algorithm, and CN Agglomerative Algorithm [310].
There is a significant gap in studies on the functional brain network in females. A considerable number of experiments were conducted in males only or in both males and females. Studies have demonstrated that there are significant differences between males and females; therefore, functional brain network studies focused solely on female participants are required to address these differences. Wang et al. [304] suggested dividing participants uniformly according to age or gender for a more accurate observation. Moreover, the number of participants in future studies should be larger in order to achieve a higher degree of generalization.

VII. CONCLUSION
This systematic literature review highlights an increasing trend in studies on functional brain connectivity networks using task-evoked EEG data. Graph theory metrics have emerged as valuable and reliable indicators for the characterization of functional interactions based on the global integration and local segregation of information processing. We demonstrate different domains in cognitive and motor functions based on an analysis of 57 articles. We also provide information regarding the distribution of selected applications, estimation techniques for functional connectivity, graph theory metrics, the number of participants, and the number of electrodes used. Furthermore, we present an overview of functional brain connectivity and the theoretical aspects of graph theory. These results provide a useful framework for the construction of an EEG functional brain network to avoid the most common pitfalls.
A larger number of reviewed studies address cognitive functions as opposed to motor processing tasks; however, studies that demonstrate the applications of brain network analyses in real-world tasks are limited and lack designs with ecological validity. Heterogeneity in experimental results, which can be attributed to a variety of factors, led to inconsistent outcomes across studies. In practice, graph theory metrics-mainly the CC and PL-are the most frequently used metrics since they reflect the functional and global integration of the brain network. Most studies on fatigue-related tasks have confirmed a reduced ability of the human brain to integrate information. Greater task difficulty results in fewer segregation processes and more integrated networks, primarily in the low-frequency bands. The presence of an economic small-world network was demonstrated for finger movement [52], the storage and retrieval of memories [233], high workload [224,225], increased time spent on tasks [107], and tasks involving mental fatigue [153]. An assessment of bias in the reviewed articles demonstrated a high level of bias risk. Addressing random sequence generation, allocation concealment, selective data reporting, and attrition should reduce the risk of such bias in future publications. In summary, connectome analyses using graph theory metrics may pave the way for new ideas in the field of neuroergonomics and ultimately lead to safer work designs. The findings of our systematic review should be useful for understanding computational methods that can be applied to the analysis of EEG data, primarily using graph theory.

VIII. CONTRIBUTIONS
The subject literature was screened, and methodological quality was assessed independently by LI and WK. Both authors provided intellectual contributions to the development and editing of the paper.