Reorganization of brain functional small‐world networks during finger movements

Abstract

A functional measure of brain organization is the efficiency of functional connectivity. The degree of functional connectivity can differ during a task compared to the rest, and to study this issue, we investigated the functional connectivity networks in healthy subjects during a simple, right‐handed, sequential finger‐tapping task using graph theoretic measures. EEGs were recorded from 58 channels in 15 healthy subjects at rest and during a motor task. We estimated mutual information values of wavelet coefficients to create an association matrix between EEG electrodes and produced a series of adjacency matrices or graphs, A, by thresholding with network cost. These graphs are called small‐world networks, and we assessed their efficiency measures. We found economical small‐world properties in brain functional connectivity networks in the alpha and beta band networks. The efficiency of the brain networks was enhanced during the task in the beta band networks, but not in the alpha band networks. A regional efficiency analysis during the task showed that the bilateral primary motor and left sensory areas showed increased nodal efficiency, Enodal, whereas decreased Enodal was found over the posterior parietal areas. The present study provides evidence for the reorganization of brain functional connectivity networks in a motor task with the greatest increase in Enodal in motor executive areas. Hum Brain Mapp, 2012. © 2011 Wiley Periodicals, Inc.

INTRODUCTION

A wide range of systems in nature can be modeled by complex networks [Albert and Barabási, 2002]. Because the brain is a complex system in which information is continuously processed and transferred to other interconnected regions with correlated functional dynamics [Sporns et al., 2000, 2004], the application of complex networks based on graph theory using EEG, MEG, and fMRI [Bullmore and Sporns, 2009] provide increased understanding of brain network organization. One useful model is small‐world networks derived from the graph theory. Watt and Strogatz [1998] have shown that small‐world networks can be characterized as a series of graphs with dense local connections and sparse long‐range connections, that is to say, despite their large size, in most small‐world networks, there is a relatively short path length between any two nodes [Albert and Barabási, 2002]. From a theoretical standpoint, small‐world network topology comprises both high clustering and short path length, which are compatible with segregated and integrated processing of the brain, respectively [Bassett and Bullmore, 2006; Sporns and Zwi, 2004]. Although the concept of a small‐world network does not carry implications about the physical distance, practically, small‐world‐like networks have been reported in brain networks of animals [Hilgetag et al., 2000; Latora and Marchiori, 2003; Yu et al., 2008] and in functional networks of the human brain [Achard and Bullmore, 2007; Salvador et al., 2005; Sporns et al., 2004]. Moreover, Bassett and Bullmore [ 2006] reported that small‐world networks can operate dynamically in a critical state [Petermann et al., 2009], facilitating rapid adaptive reconfiguration of neuronal assemblies in support of changing cognitive states.

One of the main features of small‐world networks is the tendency toward economical behavior [Latora and Marchiori, 2001]. Many small‐world networks in biology and sociology have been shown to have the economical property of delivering high global (Eglob) and local (Elocal) efficiency at relatively low cost [Latora and Marchiori, 2003]. Direct ways to measure economical parameters of brain networks were done by Achard and Bullmore [ 2007]. According to previous studies [De Vico Fallani et al., 2007; Liu et al., 2008; Wang et al., 2009], brain functional networks can be characterized by economical small‐world properties in terms of the Eglob, Elocal, and cost‐efficiency (CE) measures [Achard and Bullmore, 2007; Bassett et al., 2009]. From a methodological standpoint, the main advantage of CE is that it is independent of an arbitrary, investigator‐specified threshold [Achard and Bullmore, 2007; Bassett et al., 2009]. Reijneveld et al. [ 2007] pointed out, however, that the somewhat arbitrary threshold that is needed to convert from an association matrix to an adjacency graph maybe a problem when comparing the resulting networks. To deal with this issue, a cost threshold is used to guarantee that the graphs in both groups or conditions have the same cost (i.e., the same number of edges) and that any remaining differences in measures of graph features only reflect differences in graph organization [Stam et al., 2007a]. Otherwise, the results may be influenced by differences in the mean level of the association matrix itself.

With respect to a motor task, Eguíluz et al. [ 2005] quantitatively reported the small‐world properties in the human brain during a finger‐tapping task for the first time. In this fMRI study, they clearly showed different functional networks with robust properties across subjects and task conditions using linear correlation coefficients as an association matrix, thereby suggesting the invariant topological small‐world properties of an underlying dynamic network [Eguíluz et al., 2005]. In an MEG study, Bassett et al. [ 2006] reported the adaptive reconfiguration of the beta band networks in an index finger‐tapping task, while conserving global topological parameters such as path length and clustering coefficients similar to the results of Eguíluz et al. [ 2005]. Although previous studies have identified network reorganization with invariant small‐world properties during a finger task, the network reorganization in terms of economical properties of small‐world brain functional connectivity networks during a sequential finger‐tapping task has not been studied. Another point is that in previous studies, the correlation of time series of fMRI data [Eguíluz et al., 2005] or wavelet coefficients from MEG data [Bassett et al. 2006] was used as an association matrix presenting connectivity between two nodes. In the present study, we used a mutual information (MI) matrix of the wavelet coefficients from EEG data as an association matrix, because MI is a relatively sensitive way to reveal frequency‐specific functional connectivity compared to cross‐correlation, generalized synchronization, and phase synchronization [David et al., 2004].

In the present study, we aim to investigate the network reorganization in terms of economical properties of small‐world brain functional connectivity networks using MI during a sequential finger‐tapping task. More specifically, our questions are (1) whether there are economical small‐world properties in resting and simple sequential finger‐tapping task conditions in healthy subjects and (2) whether adaptive network reorganization occurs during a task, and, if so, (3) how it can be described with global and regional efficiency measures.

To answer to the questions, frequency band‐specific functional networks were derived from EEG data in 15 healthy subjects. Because alpha and beta band power changes have been predominantly shown to be involved in sequential finger movements [Bai et al., 2005; Gerloff, 1999], MI values of wavelet coefficients of alpha (7.97–13.10 Hz) and beta (15.05–31.25 Hz) frequency bands were used as an association matrix representing connectivity between each pair of electrodes. MI matrices were thresholded to generate a series of undirected binary graphs, and the topological properties of the networks were evaluated by graph theoretic approaches. Statistical analyses were performed to explore the differences between resting and performing a motor task.

MATERIALS AND METHODS

Participants

The study involved 15 right‐handed healthy subjects (mean age of 45.9 years; 12 males). They were recruited from the NIH volunteer pool. The protocol was approved by the Institutional Review Board; all subjects gave their written informed consent for the study.

EEG Acquisition and Preprocessing

EEG signals were recorded from 58 surface electrodes mounted on a cap (Electro‐Cap International, Eaton, OH) using the international 10–20 system referenced to the right earlobe electrode (A2). Before further analysis to reliably estimate the scalp EEG potential [Nunez and Srinivasan, 2006], EEG signals were re‐referenced to the digitally linked earlobe reference with the left earlobe electrode (A1), which was recorded as a separate channel. Bipolar recordings of the vertical and horizontal electrooculogram (EOG) were recorded and used for artifact correction. Surface electromyograms from the extensor digitorum communis, flexor digitorum superficialis, and the first dorsal interosseus muscles were also simultaneously recorded to monitor subject finger movements. Signals from all channels were amplified (Neuroscan, El Paso, TX), filtered (DC‐100 Hz) and digitized with sampling frequency 1 kHz.

Resting state EEGs were recorded for 5 min with eyes open. For the simple sequential finger‐tapping task, subjects were asked to press the button of a commercial keypad (Neuroscan, El Paso, TX) with their right hand paced by a metronome beat at 2 Hz for 5 min. The sequence performed was 2‐3‐4‐5 with each digit corresponding to index, middle, ring, and little finger, respectively. Subjects were instructed to keep their eyes fixed on a cross 3 m in front of them during the entire recording to avoid eye movements and visual feedback.

During preprocessing, the linear trend was removed from the entire epoch, and eye movement‐related artifacts were corrected using an autoregressive exogenous input model with EOG signals as the exogenous inputs. These preprocessing steps were performed using the same homemade MATLAB (MathWorks, Natick, MA) scripts as previously used in Bai et al. [ 2005]. Finally, five artifact‐free epochs (epoch length 10 s) in each subject were obtained to calculate wavelet coefficients. Before applying wavelet transformation, EEG was downsampled to 500 Hz.

Spectral Power Analysis

To look at the spectral power change during the motor task, a fast Fourier transformation with Hamming window was performed for each 1024 ms epoch and all electrodes. The power spectrum from 1 to 100 Hz was calculated for each epoch and averaged across epochs. To account for intersubject variability, task‐related power (TrPow) was expressed as the percent change of spectral power during the task (Pow_task) compared to spectral power during the rest condition (Pow_rest) and normalized according to the equation [Gerloff et al., 1998; Hummel et al., 2002]

TrPow increases are expressed as positive values, while task‐related decreases are expressed as negative values. Alpha and beta band power changes were calculated by averaging the power values of the respective frequency bins. Group grand averages of percentage power changes were then calculated.

Mutual Information

Because David et al. [ 2004] showed that MI is a measure of frequency band‐limited functional connectivity with good sensitivity, we estimated MI values of wavelet coefficients to create an association matrix between the EEG electrodes. Wavelet coefficients of alpha (7.97–13.10 Hz) and beta (15.05–31.25 Hz) frequency bands were obtained from Morlet wavelet transformation. These computations were performed using the wavelet toolbox in MATLAB (MathWorks, Natick, MA). MI was calculated using the following equation:

where p(X(t), Y(t)) is the joint probability density function (PDF) between X(t) and Y(t). For construction of the approximated PDF, 32 bins were adopted for 4,096 samples. We took the logarithm with base two, so maximum MI in our study is five bits.

A corrective term to compensate the effect of finite data and quantization on the PDF was added, because the calculated entropy and MI are functionally dependent on the amount of data and the quantization chosen [Roulston, 1999].

where B _X and B _Y are the numbers of bins for which p(X) > 0 and p(Y) > 0, B _XY is the number of bins for which p(X,Y) > 0, and N is the size of the time series. MI_true is the corrected MI, which is accepted as a final MI value.

To look at the task‐related MI changes as done for power spectral changes, a task‐related MI (TrMI) was calculated in the same manner as TrPow.

A positive TrMI implies an increase of MI during a task and vice versa.

Graph Construction

To yield a series of adjacency matrices or graphs A, the MI association matrix was thresholded by network cost as used in previous studies [Achard and Bullmore, 2007; Bassett et al., 2009; Latora and Marchiori, 2001; Wang et al., 2009].

The degree of each node is defined as the number of edges connecting it to the rest of the graph. Degree of connectivity of a graph is the average of the degrees of all the nodes in the graph. A connection density or network cost K can be defined as , where N denotes the number of nodes (here, 58), and corresponds to the total number of edges in the adjacency matrix A. An unweighted graph A and undirected edges between nodes were constructed by applying cost, K, to the MI association matrix of wavelet coefficients of each subject at each condition. Element of A is given by , where θ is the Heaviside function, defined as 1 if x ≥ 0, and otherwise 0.

Thresholding of all MI matrices was started at the cost of 0.16 to construct a sparse graph with the mean degree 2 log(N) ≈ 9, equivalent to cost K ≈ 0.16 or 16% of the maximum number of edges possible in a network of 58 nodes similar to the method used in previous studies [Achard and Bullmore, 2007; Bassett et al., 2006; Liu et al., 2008]. A small‐world regime was determined by the criteria set forth by Achard and Bullmore [ 2007], that is, that small‐world properties of the brain networks are diagnosed by Eglob greater than a comparable regular (but less than a random graph) and Elocal greater than a random graph (but less than a regular). Comparable 20 regular graphs that preserved the same number of nodes and edges were synthesized. Random graphs (here, 20) were derived by randomly rewiring the links of the original networks while keeping the same degree distribution [Maslov and Sneppen, 2002]. The same criteria for small‐world regime were used as in other previous studies [Liu et al., 2008; Wang et al., 2009].

For the analysis of weighted networks, a recently proposed method by Stam et al. [2009] would be a good alternative, because it avoids setting a threshold for an association matrix to make adjacent matrices or graphs. Although efficiency measures used in the present study are independent of an arbitrary, investigator‐specified threshold [Achard and Bullmore, 2007; Bassett et al., 2009], it is noteworthy that by fixing the cost, edges in the graph may be created based upon weak or even nonsignificant connectivity values. To avoid the hidden bias, the association matrix went through two steps of thresholding considering both the cost and connectivity value. The first step is done by MI values, which produce cost values at each threshold. New threshold values were found corresponding to a fixed cost of interest by interpolation. Second, the association matrix was rethresholded by the new threshold, which we obtained from the previous step.

In addition, a small‐worldness index called sigma, was also examined to clarify whether small‐worldness is achieved within the small‐world regime by conventional methods. By definition, small‐world networks have similar path lengths (L _p) but greater clustering coefficients (C _p) when compared with random networks. That is, if a random network has a clustering coefficient C ${}_{\text{p}}^{\text{rand}}$ and path length L ${}_{\text{p}}^{\text{rand}}$, then γ = C _p/C ${}_{\text{p}}^{\text{rand}}$ ≫ 1 and γ = L _p/L ${}_{\text{p}}^{\text{rand}}$ ≈ 1 [Watts and Strogatz, 1998]. Thus, small‐worldness index could be defined as sigma, σ = γ / λ (where γ = C _p/C ${}_{\text{p}}^{\text{rand}}$, γ = L _p/L ${}_{\text{p}}^{\text{rand}}$), which is greater than 1 if the network has small‐world properties [Humphries and Gurney, 2008; Humphries et al., 2006]. C ${}_{\text{p}}^{\text{rand}}$ and L ${}_{\text{p}}^{\text{rand}}$ were obtained by averaging 20 populations of random networks. It is of note that because we checked that Eglob and Elocal values are not significantly affected by the population of random networks, 20 random networks were created for the comparison.

Efficiency Measures of Small‐World Networks

For each cost in the range 0.16 < K < 1.0, global efficiency, Eglob, indicating the efficiency of a parallel information transfer in the whole network [Latora and Marchiori, 2001, 2003], was calculated as , where i ≠ j denotes a region connected to i, and d _i,j is the shortest length of the path from node i to node j. As another global measure, local efficiency, Elocal can be defined as , where A _i is the subgraph of the neighbors of a node i, and E (A _i) indicates the efficiency of the subgraph A _i. By definition, Elocal can be understood as a measure of the fault tolerance of the network, indicating how efficient the communication is between the first neighbors of i when i is removed [Achard and Bullmore, 2007; Latora and Marchiori, 2001].

Eglob and Elocal are measures of global information flow, whereas regional efficiency, Enodal, was used to assess the efficiency at each node. Enodal can be likewise defined as the inverse of the harmonic mean of the minimum path length between a node i and all other nodes in a graph [Achard and Bullmore, 2007]. It is regarded as a measure of the communication efficiency between a node i and all the other nodes in the network [Wang et al., 2009].

The global CE is defined as the difference between Eglob and cost, Eglob‐K, which will be positive in the case of an economical network [Achard and Bullmore, 2007; Bassett et al., 2009; Wang et al., 2009]. The clustering, path length, and efficiency estimates were obtained with functions from the Brain Connectivity Toolbox (http://www.brain-connectivity-toolbox.net/).

Statistical Analysis

Normality of the small‐world parameters was graphically assessed by plotting. Because all plots are linear over the selected cost range, the variables are regarded as having normal distribution. We compared the global metrics (mean MI, Eglob, Elocal, CE) at each cost value to evaluate the small‐world topological differences between conditions using a two‐tailed paired t‐test; P values <0.05 are considered as significant.

For the Enodal distribution (at a cost of 0.28), the connectivity map was standardized by converting to Z scores for the condition before group averaging to reduce intersubject variability. P values <0.05 (uncorrected) are considered as significant. Uncorrected P‐values are accepted instead of using correction for multiple comparisons, because there are many comparisons, and we desired a hypothesis‐free exploration of the data. Hence the findings should be formally considered descriptive, and the findings here can be used as an a priori hypothesis in further studies.

All statistical analysis was performed using Statistics Toolbox in MATLAB (MathWorks, Natick, MA). For network visualization, Pajek software [De Nooy et al., 2005] was used. The scalp plotting program used in the present study was adapted for the current use from Delorme et al. [ 2007] Headplot MATLAB script.

RESULTS

We extracted 120 trials of the four‐item sequences equivalent to a total of 480 key presses. The exact sequence of key presses was used to assess performance accuracy; mean performance accuracy was 95.76% with standard deviation of 0.03%.

Figure 1 presents TrPow and TrMI changes. There are TrPow decreases over centro‐parietal areas in the alpha band and fronto‐central areas in the beta band (Fig. 1a,b). On the other hand, TrMI increases are shown over almost all areas in both alpha and beta bands. Increased TrMI in the beta band is more profound over anterior than posterior regions.

Figure 1.

Task‐related power (TrPow) and MI (TrMI) changes in alpha and beta band. Decreased TrPow over centro‐parietal regions in the alpha (a) and fronto‐central regions in the beta band (b) are found. Increased TrMI are shown (c, d). Increase of TrMI in the beta band is more profound over anterior than posterior region.

Table I presents all the mean MI values in the alpha and beta band networks at rest and with the task. Although the mean MI values were increased during the task in both the alpha and beta band networks, no significant difference was found in mean MI values of the alpha band networks (P = 0.201 in accordance with a Table I). On the other hand, beta band networks increased significantly (P = 0.012).

Table I.

Mean MI values in the alpha and beta band networks at rest and during task

Band	Rest	Task	t	P
Alpha	0.633 ± 0.023	0.663 ± 0.019	–1.341	0.201
Beta	0.455 ± 0.017	0.495 ± 0.025	–2.871	0.012

All values presented as mean ± SEM.

Figure 2 shows Eglob and Elocal as functions of cost for the random, regular, and brain networks. The random graph has a greater Eglob than the regular, and the regular has a greater Elocal than the random graph. As for the brain networks, on average, the alpha and beta band functional networks have efficiency curves located between the limiting cases of random and regular topology (Fig. 2a–d). Thus, according to the criteria [Achard and Bullmore, 2007], the small‐world regime could be conservatively defined as the range of costs 0.16 < K < 0.5 in the alpha and beta band networks for which the Eglob curve for both groups is greater than the Eglob curve for the regular and less than random networks. Importantly, Eglob during a task was consistently larger than that in the resting state, and the smallest P‐value was found at a cost of 0.28 (P = 0.029, bold in Table II). On the other hand, no significant changes in Elocal were revealed.

Figure 2.

Eglob (a, c) and Elocal (b, d) as a function of cost for the random, regular, and brain networks in the alpha (a, b) and beta (c, d) band functional connectivity networks. Small‐world regime can be defined as the range of costs 0.16 < C < 0.5 for which the Eglob curve for both conditions is greater than the Eglob curve for the regular and less than random networks (a, c), and for which the Elocal curve for both conditions is greater than the Eglob curve for the random and less than regular networks (b, d). Note that the smallest P‐value was found at a cost of 0.28 (P = 0.029). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Table II.

Eglob in the beta band networks at rest and during task

Cost	Rest	Task	t	p
0.26	0.516 ± 0.009	0.537 ± 0.005	−2.097	0.055
0.28	0.537 ± 0.008	0.557 ± 0.006	−2.424	0.029
0.30	0.558 ± 0.008	0.574 ± 0.006	−1.840	0.087
0.34	0.596 ± 0.008	0.612 ± 0.008	−1.920	0.075

All values presented as mean ± SEM.

Small‐worldness index, sigma, in the small‐world regime for the alpha and beta band networks is shown in Figure 3. All sigma were larger than 1, which means the alpha and beta band networks have a small‐world organization according to the criteria of Humphries et al. [ 2006].

Figure 3.

Plot showing the mean and SEM (standard error of mean) of small‐worldness index, sigma, as a function of cost in the alpha (a) and beta (b) band functional connectivity networks. Because sigma is >1 in the small‐world regime (0.16 < C < 0.5), the alpha and beta band networks both at rest and during task performance can be considered as small‐world networks. No significant changes were found at any cost threshold. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Regarding global CE, the alpha and beta band networks have positive values in a given small‐world regime (see Fig. 4). This result implies that the alpha and beta brain networks in both conditions have economical functional networks, because efficiency was greater than cost. Note that the smallest P‐value was found at a cost of 0.28.

Figure 4.

Global CE as a function of cost for the random, regular, and brain networks. In the small‐world regime, 0.16 < C < 0.5, for the alpha and beta band networks, the CE curve for both groups is greater than the CE curve for the regular and less than random networks. Note that the smallest P‐value was found at a cost of 0.28 (P = 0.029). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Because the increased Eglob and CE with the smallest P‐value were found at a cost of 0.28, regional efficiency, Enodal, was tested at a cost of 0.28 to investigate further the changes in regional nodal characteristics of the functional networks. Upper panel of Figure 5 demonstrates the beta band functional networks at a cost of 0.28 during rest and the task conditions. Increased connections from bilateral motor areas C3 and C4 to the rest of the brain regions are recognizable. We tried to find main nodes that gave significant differences between conditions, because these nodes could be regarded as the neural correlates characterizing the reorganization in brain functional networks in a motor task. By definition, a node with high Enodal will have a short minimum path length to all other nodes in the graph. The lower panel of Figure 5 depicts the task‐related network changes describing which regions have increased or decreased connections. There are increased connections over bilateral primary motor, sensorimotor, and frontal areas, whereas decreased connections were found over the posterior parietal areas. It seems that long range connections including interhemispheric connections emerged during the task.

Figure 5.

Beta band functional connectivity networks at rest (upper left panel) and during task performance (upper right panel) at a cost of 0.28. Connections from posterior regions to the rest the regions are decreased, whereas connections from sensorimotor areas to the rest of the regions are increased during a task. Blue lines indicate connections from the bilateral motor regions C3 and C4 to the rest of the regions which increased during task. Lower panel shows the task‐related network changes. The increased connections (solid lines) over bilateral primary motor, sensorimotor, and frontal areas are shown, whereas decreased connections (dotted lines) were found over the posterior parietal areas.

Figure 6 represents the t and P maps of Enodal. Bilateral primary motor and the left sensorimotor areas showed increased Enodal, whereas decreased Enodal was found over the posterior parietal areas during a task. Detailed t and P values are shown in Table III.

Figure 6.

First row represents group‐averaged topographic t value maps of Enodal from the left, top, and right views. Red indicates enhanced Enodal, while blue indicates diminished Enodal during a task when compared with rest. Bilateral primary motor and the left sensorimotor areas showed increased Enodal, whereas decreased Enodal was found over the posterior parietal areas. Second row indicates P maps of Enodal from the left, top and right views. Each point corresponds to the location shown in Table III, indicating significant changes. Predominant changes were found at C3 (P = 0.006) and C4 channels (P = 0.005).

Table III.

Nodes showing significant changes in Enodal, at a cost of 0.28 corresponding to the smallest P‐value indicating an increase of Eglob

Location	Rest	Task	t	P
Increased Enodal during the task
FC1	0.485 ± 0.063	0.659 ± 0.040	−2.823	0.014
FC3	0.304 ± 0.045	0.466 ± 0.037	−2.597	0.021
C3	0.490 ± 0.053	0.689 ± 0.046	−3.224	0.006
C4	0.542 ± 0.060	0.748 ± 0.057	−3.359	0.005
CP1	0.955 ± 0.028	1.055 ± 0.032	−2.922	0.011
CP3	0.587 ± 0.065	0.700 ± 0.043	−2.389	0.032
Decreased Enodal during the task
P5	0.239 ± 0.066	0.121 ± 0.065	2.543	0.023
POz	0.661 ± 0.037	0.548 ± 0.049	2.881	0.012
PO3	0.326 ± 0.069	0.229 ± 0.063	2.332	0.035
PO4	0.369 ± 0.063	0.274 ± 0.064	2.227	0.043

All values presented as mean ± SEM (standard error of mean).

DISCUSSION

We investigated functional connectivity networks using graph theoretic measures to assess economical features in healthy subjects during a motor task.

We found that mean MI values in the beta band functional networks were significantly increased during the task, but not in the alpha band networks. Enhanced MI could be explained by a higher demand for information transfer during a task, because MI has been used as a measure of functional connectivity indicating information flow [Jin et al., 2006a, b]. Beta oscillations are important in long‐range synchronization for optimal information processing in large‐scale networks [Gail et al., 2004; Tallon‐Baudry et al., 2001, 2004], and this is supported by computational modeling [Kopell et al., 2000]. It has been shown that its periodicity is long enough to coordinate neuronal activity in distant cortical regions that may be separated in time by an appreciable axonal conduction delay [Kopell et al., 2000]. In the motor system, beta oscillations play an important functional role in motor control [Schnitzler and Gross, 2005]. Thus, our results indicating increased mean MI values in the beta band functional networks suggest that performing a simple sequential finger‐tapping task is associated with information transmission through long‐range synchronization mediated by beta oscillations between neural assemblies. Concerning the analysis based on graph theory, these MI matrices were thresholded by cost to yield a series of adjacency matrices A. This makes it possible to control the effects of different mean levels of MI values on network organization [Stam et al., 2007a].

In agreement with previous studies [Achard et al., 2006; Bassett and Bullmore, 2006; Bassett et al., 2009; Liu et al., 2008; Wang et al., 2009], the small‐world properties of the brain functional networks during both rest and task conditions were found over a wide cost range in the alpha and beta band networks, because the efficiency curves of brain networks of both conditions were located between the curves of the random and regular graphs (see Fig. 1). More directly, because all small‐worldness indices, sigma, were larger than 1 in the small‐world regime, which was defined by Figure 2, the alpha and beta band networks clearly demonstrate a small‐world organization. Moreover, small‐world features were preserved even in a motor task, which is in line with previous studies indicating an invariant small‐world topology during an index finger‐tapping task [Bassett et al., 2006; Eguíluz et al. 2005]. In addition to the invariant small‐world network properties, the functional small‐world networks showed economical properties (see Fig. 3), consistent with previous studies showing the existence of economical small‐world networks in the human brain [Achard and Bullmore, 2007; Bassett et al., 2009; Liu et al., 2008; Wang et al., 2009]. Moreover, enhanced Eglob and CE at a cost of 0.28 were found, while no significant changes in Elocal were revealed. Considering that Eglob and Elocal can represent the functional integration and segregation, respectively [Latora and Marchiori, 2001], our result suggests enhanced functional integration in the beta band networks during a task. Taken together, we found economical small‐world properties in brain functional connectivity networks in the alpha and beta band networks. Moreover, the efficiency of the brain networks was enhanced during the task in the beta band network. It is of note that the upper alpha band (10.16–13.10 Hz) corresponding to the mu band and, therefore, likely to be related to movements showed almost the same results as the full alpha band (data not presented).

Network topology can be changed through a combination of four elementary processes: addition or removal of a node and addition or removal of an edge [Albert and Barabási, 2002]. In a biological context, highly evolved nervous systems are capable of rapid, real‐time integration of information across segregated brain regions, which is accomplished by dynamic functional interactions in large‐scale networks of the brain [Sporns and Honey, 2006]. Much evidence supports the idea that perception and cognition depend on patterns of dynamic binding of distant neural assemblies, which reflect changes in sensory inputs or task demands [Bassett et al., 2006; Mima et al., 2001; Singer, 1999; Varela et al., 2001]. With respect to the functional networks during a motor task, previous studies consistently suggested the adaptive reconfiguration of brain networks with invariant small‐world properties. Eguíluz et al. [ 2005] reported that the small‐world properties were robust across task conditions, although the topographic distribution of the functional networks was very different depending on the tasks. In addition, clustering coefficient and characteristic path length were preserved in a motor task, while brain functional networks demonstrated the task‐related spatial reconfiguration [Bassett et al., 2006]. These results support one of the main features of small‐world networks presenting the ability to operate dynamically facilitating rapid adaptive reconfiguration of neuronal assemblies depending on states [Bassett and Bullmore, 2006]. Although Eguíluz et al. [ 2005] and Bassett et al. [ 2006] demonstrated an adaptive reorganization of the functional networks during a motor task, these studies did not directly describe the network from an economical small‐world standpoint. However, our results provide further evidence for the reorganization of the small‐world networks during a motor task using efficiency measures. More importantly, because we found the network reorganization within subjects, our study provides further results to support the adaptive reorganization of the functional networks depending on the task as suggested by Bassett et al. [ 2006] work performed between subjects. Recent studies [Bassett et al., 2006, 2009; De Vico Fallani et al., 2007] have described the interdependence of network organization and behavior. Our findings contribute to accumulating evidence of economical small‐world network behavior and its reorganization during a motor task.

To investigate which areas manifested the network reorganization, Enodal was also evaluated at a cost of 0.28 corresponding to the cost with the smallest P‐value indicating increase of Eglob. Increases of Enodal were revealed in bilateral primary motor and the left sensorimotor areas, which could be interpreted as the demand for functional connectivity to maintain motor command and subsequent execution. The most profound changes were found at C3 and C4 channels, corresponding to the contra‐ and ipsilateral primary motor areas. Our results agree with previous studies reporting the involvement of the primary sensorimotor cortex during finger‐tapping tasks [Bai et al., 2005; Witt et al., 2008]. Particularly, Witt et al. [ 2008] showed consistent activation of the primary sensorimotor cortex in activation likelihood estimation meta‐analysis using fMRI and PET studies. In addition, the involvement of the primary sensorimotor cortex during sequential finger movements was found in an EEG study [Bai et al., 2005].

On the other hand, the decreases of Enodal over posterior parietal regions were observed in the present study, although the posterior parietal cortex has been shown to be active during both the execution and production of complex sequential motor tasks [Boecker et al., 1998; Gordon et al., 1998; Honda et al., 1998; Sadato et al., 1996; Sakai et al., 1998]. Our results indicating the decreases of Enodal over posterior regions might be due to the absence of given feedback of the performance and the task's simplicity. Many studies that reported activation of the parietal lobe used visual feedback [Boecker et al., 1998; Gordon et al., 1998; Honda et al., 1998; Sakai et al., 1998], which is related to the evaluation of self‐generated movements [MacDonald and Paus, 2003]. In contrast, in the present study, subjects were instructed to keep their eyes fixed during the entire recording to avoid visual feedback, so that evaluation of self‐generated movements may not have been required. In addition, involvement of the parietal area has been correlated with the complexity of the sequential motor task [Boecker et al., 1998; Sadato et al., 1996]. It appears that our task was sufficiently simple so as not to involve the parietal areas unlike some previous studies.

The significant efficiency changes were found in the beta functional connectivity network, but not in the alpha band networks during a task. This is a conceivable result, because it was suggested that the beta band has a specific role in movements in either EEG studies [Mima et al., 2000; Serrien and Brown, 2002; Serrien et al., 2003] or MEG studies [Gross et al., 2005]. Although many studies have showed that the movement‐related power changes occurred prominently in both the alpha (7–13 Hz) and beta frequency range (13–30 Hz) [Leocani et al., 1997; Pfurtscheller et al., 1997a, b; Bai et al., 2005), the topographic and temporal evolution of changes in these two frequency ranges [Pfurtscheller et al., 1997b; Manganotti et al., 1998] are not identical. This means that they are thought to represent different aspects of movement execution. However, these previous studies are limited to looking at the changes of predefined relevant regions by using a univariate analysis method, which could explain a functional segregation. On the other hand, the application of graph theoretical analysis to sensorimotor task‐related functional networks would be helpful in extending our understanding of sensorimotor processing in terms of functional integration. As for the network analysis, the beta band functional networks in the finger‐tapping task would favor their rapid, adaptive reconfiguration in the face of changing environmental demands [Bassett et al., 2006].

The main advantage of studying a brain network from the framework of graph theory is that it can provide an overall sense of the complexity of the network and characterize connection patterns within the brain from a perspective of topological organization [Wang et al., 2010), unlike MI analysis that can only describe the relationships between pairs of electrodes. In addition, we found a reorganization of the beta band brain network, which could not be revealed from a bivariate analysis such as MI. Although the MI result per se showed the increased functional connectivity in the beta band as shown in Table I, by virtue of graph theoretic analysis, it is possible to better understand how the brain network functions.

One limitation of the present study is that the well‐known bias of the effects of volume conduction in functional connectivity studies of EEG may influence the estimation of graph theoretical measures. Because of volume conduction, nearby EEG sensors are likely to display high connectivity between them, which may cause a spurious estimation of the parameters, for example, clustering coefficients. Although it is difficult to know exactly how much volume conduction would impact on network parameters, this effect might be minimized based on the following point. The relative changes were considered rather than taking an absolute value of measures, which is in line with the claim of Alonso et al. [2010] pointing out that the effects of field spread could be considered identical in all conditions. By using time‐delayed MI [Jin et al., 2006a, b, 2010], this problem could be reduced, because volume conduction has no time lag. Other possible solutions include the imaginary part of coherency [Nolte et al., 2004] or phase lag index measure [Stam et al., 2007b].