Scholarly article on topic 'Graph Analysis of EEG Resting State Functional Networks in Dyslexic Readers'

Graph Analysis of EEG Resting State Functional Networks in Dyslexic Readers Academic research paper on "Clinical medicine"

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Clinical Neurophysiology
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{"Electroencephalography (EEG)" / "Functional connectivity" / Network / "Graph theory" / "Minimum spanning tree" / Dyslexia}

Abstract of research paper on Clinical medicine, author of scientific article — G. Fraga González, M.J.W. Van der Molen, G. Žarić, M. Bonte, J. Tijms, et al.

Abstract Objective Neuroimaging research suggested a mixed pattern of functional connectivity abnormalities in developmental dyslexia. We examined differences in the topological properties of functional networks between 29 dyslexics and 15 typically reading controls in 3rd grade using graph analysis. Graph metrics characterize brain networks in terms of integration and segregation. Method We used EEG resting-state data and calculated weighted connectivity matrices for multiple frequency bands using the phase lag index (PLI). From the connectivity matrices we derived minimum spanning tree (MST) graphs representing the sub-networks with maximum connectivity. Statistical analyses were performed on graph-derived metrics as well as on the averaged PLI connectivity values. Results We found group differences in the theta band for two graph metrics suggesting reduced network integration and communication between network nodes in dyslexics compared to controls. Conclusion Collectively, our findings point to a less efficient network configuration in dyslexics relative to the more proficient configuration in the control group. Significance Graph metrics relate to the intrinsic organization of functional brain networks. These metrics provide additional insights on the cognitive deficits underlying dyslexia and, thus, may advance our knowledge on reading development. Our findings add to the growing body literature suggesting compromised networks rather than specific dysfunctional brain regions in dyslexia.

Academic research paper on topic "Graph Analysis of EEG Resting State Functional Networks in Dyslexic Readers"

Accepted Manuscript



Graph Analysis of EEG Resting State Functional Networks in Dyslexic Readers

G. Fraga González, M.J.W. Van der Molen, G. Zaric, M. Bonte, J. Tijms, L. Blomert, C.J. Stam, M.W. Van der Molen

S1388-2457(16)30453-9 http://dx.doi.Org/10.1016/j.clinph.2016.06.023 CLINPH 2007888

To appear in:

Clinical Neurophysiology

Accepted Date:

8 June 2016

Please cite this article as: Fraga González, G., Van der Molen, M.J.W., Zaric, G., Bonte, M., Tijms, J., Blomert, L., Stam, C.J., Van der Molen, M.W., Graph Analysis of EEG Resting State Functional Networks in Dyslexic Readers, Clinical Neurophysiology (2016), doi:

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1 Graph Analysis of EEG Resting State Functional Networks in

2 Dyslexic Readers

3 Fraga González, G. -1 , Van der Molen, M.J.W.Z'J, Zaric, G. Bonte, M. Tijms, J.

der Molen, M.J.W.2,3, Zaric, G. 4, Bonte, A T 4 4 Blomert, L. 4,t, Stam, C.J. 6, Van der Molen, M.W. 1,7

6 1 Department of Psychology, University of Amsterdam, The Netherlands

7 2 Leiden University, Institute of Psychology, The Netherlands

rlands rlands

8 Leiden Institute for Brain and Cognition, Leiden University, The Netherlands

9 4 Department of Cognitive Neuroscience, Faculty of Psychology and Neuroscience,

10 University of Maastricht, The Netherlands

11 5 IWAL Institute, Amsterdam, The Netherlands

12 6 Department of Clinical Neuropsychology and MEG Center, Neuroscience Campus Amsterdam, VU

13 University Medical Center, Amsterdam, The Netherlands

14 7 Amsterdam Brain and Cognition, University of Amsterdam, The Netherlands

20 * Correspondence:

21 Gorka Fraga Gonzalez (Ph.D.)

22 Department of Psychology ,University of Amsterdam, Nieuwe Achtergracht 129B, 1018 WS

23 Amsterdam, The Netherlands

24 E-mail:

29 1 Leo Blomert passed away on November 25, 2012.

u: u.rrai

19 f Lec


Organization of brain networks in dyslexies and typically-reading controls. Minimum spanning tree (MST) graphs were derived from connectivity matrices. Graph metrics in the theta-band showed less integrated network configuration in dyslexics.

40 Objective


41 Neuroimaging research suggested a mixed pattern of functional connectivity abnormalities in

42 developmental dyslexia. We examined differences in the topological properties of functional

43 networks between 29 dyslexics and 15 typically reading controls in 3rd grade using graph

44 analysis. Graph metrics characterize brain networks in terms of integration and segregation.

45 Method

46 We used EEG resting-state data and calculated weighted connectivity matrices for multiple

47 frequency bands using the phase lag index (PLI). From the connectivity matrices we derived

48 minimum spanning tree (MST) graphs representing the sub-networks with maximum connectivity. Statistical analyses were performed on graph-derived metrics as well as on the

50 averaged PLI connectivity values.

51 Results

52 We found group differences in the theta band for two graph metrics suggesting reduced

53 network integration and communication between network nodes in dyslexies compared to

54 controls.

55 Conclusion

56 Collectively, our findings point to a less efficient network configuration in dyslexics relative

57 to the more proficient configuration in the control group.

58 Significance

59 Graph metrics relate to the intrinsic organization of functional brain networks. These metrics

60 provide additional insights on the cognitive deficits underlying dyslexia and, thus, may

61 advance our knowledge on reading development. Our findings add to the growing body

62 literature suggesting compromised networks rather than specific dysfunctional brain regions

63 in dyslexia.

66 (EEG), ^ ^ gKph ^

67 minimum spanning tree, dyslexia.

70 Introduction

71 Reading involves integrated functioning of complex brain networks. Distinct brain

72 systems, mostly in the left hemisphere, have been proposed to specialize during reading

73 acquisition (see a review in Schlaggar and McCandliss, 2007). Studies in developmental

74 dyslexia revealed various disturbances of the brain networks implicated in reading. Studies

75 using diffusion tensor imaging (DTI) to examine white matter properties of the main

76 pathways that constitute the anatomical basis of the network reported reduced connectivity in

77 dyslexia (for a review and meta-analysis Vandermosten et al., 2012). Similarly, a score of

78 functional magnetic resonance imaging (fMRI) studies in adults reported reduced

79 connectivity of the reading network (e.g., Pugh et al., 2000; Quaglino et al., 2008; Schurz et

80 al., 2014; Shaywitz et al., 2003; Stanberry et al., 2006; Van der Mark et al., 2011; but see

81 Richards and Berninger, 2008) and other connectivity disturbances (Finn et al., 2014; Wolf et

82 al., 2010). A recent MRI study examining the topological organization in Chinese dyslexic

83 children revealed a less integrated network organization relative to typically reading controls,

84 characterized by increased local processing and less long-range communication (Liu et al.,

85 2015).

86 The neural network studies highlight the interactive nature of brain systems implicated in

87 reading and underscore the relevance of connectivity to the study of dyslexia. Although

88 specific brain regions have been successfully linked to literacy acquisition, the understanding

89 of a highly complex cognitive function such as reading may also require a more integrative

90 and

holistic view of brain function, which can be conceptualized as a complex network

91 (Bullmore and Sporns, 2009). In relation to this, previous neuroimaging research showed that

92 examining the dynamics of spontaneous (task independent) activity in the brain provide us

93 with meaningful information about how different brain areas communicate (van den Heuvel

94 and Hulshoff Pol, 2010) and the underlying architecture of functional brain networks

95 (Gusnard and Raichle, 2001).

96 The goal of the current study was to examine global functional network connectivity and

97 organization in developmental dyslexia using the electroencephalogram (EEG) in resting-

98 state data. Previous fMRI studies on resting-state data revealed relations between resting-

99 state functional connectivity across the reading network with reading abilities in children and

100 adults (Koyama et al., 2011, 2013; Schurz et al., 2014; Zhang et al., 2014). Other studies

101 linked the strength of resting-state connectivity between the visual word recognition areas

102 and the dorsal attention network to age and reading skills (Vogel et al., 2012; Vogel et al.,

103 2014). The latter studies attest to the utility of resting-state data to characterize the functional

104 reading network (Hampson et al., 2006; Koyama et al., 2010).

105 In the current study we used graph analysis, which allows for modeling the organization of

106 resting-state whole-brain functional connectivity networks during development (Stam, 2014).

107 A 'graph' refers to an abstract representation of a network, consisting of a set of nodes

108 (vertices) and connections between them (edges). Various graph measures allow for

109 characterizing graph topologies in terms of the efficiency of information transfer and an

110 optimal balance between 'segregation' and 'integration' (see reviews in Bullmore and

111 Sporns, 2009; Bullmore and Sporns, 2012). Thus, a 'small-world' network topology,

112 characterized by a high clustering (related to high local connectedness and robustness) and a

113 short path length (related to high global efficiency) has been proposed as a plausible

114 configuration of highly efficient brain networks (Bassett and Bullmore, 2006). This topology

115 combines features from ordered or regular networks (high clustering) and random networks

116 (short path length).

117 A recent development in graph theory refers to minimum spanning tree (MST) analysis

118 (Stam et al., 2014). A tree is a loop-less sub-graph derived from a weighted connectivity

119 matrix, with a fixed number of nodes and edges; in the MST, the presence of a link is not

120 defined by a given threshold in the connectivity weights (see Methods). The advantage of

121 MST analysis over conventional graph procedures is that it minimizes bias when performing

122 direct comparisons between groups and experimental conditions (Tewarie et al., 2015). There

123 are two extreme tree topologies; path- and star-like configurations. Path-like confi gurations

124 consist of nodes that are all linked to two other nodes with the exception of the nodes at

125 either end of the path. Nodes with only one link in a tree are referred to as 'leaf' nodes (or

126 leaves) and the number of those nodes in a tree is the leaf number. Thus a path has a leaf

127 number of two. In contrast, star-like configurations consist of a central node connected to all

128 other nodes with only one link. Thus, a star consisting of N nodes has a leaf number of N-1.

129 Many different tree topologies are in between the two extreme configurations and they can be

130 characterized using a variety of metrics (review in Van Mieghem, 2014). We will apply the

131 tree measures that have been applied previously in EEG studies (see Methods section below).

132 The MST analysis has been successfully applied to EEG data from different populations.

133 A relatively early study indicated that patients with left vs. right temporal epilepsy could be

134 reliably discriminated in terms of large scale functional networks emerging just prior to the

135 onset of seizures (Lee et al., 2006). More recently, Fraschini et al., 2014 examined the effects

136 of vagal nerve stimulation in patients with pharmaco-resistant epilepsy. MST analysis yielded

137 a clear differentiation between responders vs. non-responders. Vagal nerve stimulation

138 shifted the network towards a more star-like network architecture in responders but not in

139 non-responders. Van Diessen et al., 2014 examined the effect of sleep deprivation on EEG

140 networks in children diagnosed with focal epilepsy. MST analysis revealed a shift to a more

141 path-like topology after sleep deprivation in children with focal epilepsy whereas a shift

142 towards a more star-like configuration was observed in controls. Vourkas et al., 2014

143 performed a MST analysis on the EEG recorded in children with mathematical difficulties

144 and typical controls during the performance of tasks with increasing difficulty. Although

145 group differences were absent in this study the MST parameters suggested a more centralized

146 and integrated network layout in the alpha bands of the EEG with increasing task demands.

147 Most relevant to the present study, Boersma et al., (2013) applied MST analysis to resting-

148 state EEG data of a large sample of 5- and 7-years old children. Developmental change was

149 observed for the EEG alpha band. More specifically, the MST analysis yielded increases in

150 diameter and eccentricity with advancing age while leaf number, degree and hierarchy

151 decreased. This pattern of results was interpreted to suggest a more integrated network

152 configuration in the 7- compared to the 5-years olds.

153 Collectively, the MST studies suggest this approach may provide a sensitive tool to assess

154 condition or group differences in network configuration. Previously, graph analysis of

155 magnetoencephalogaphic (MEG) data in dyslexic children and controls showed task-

156 dependent dysfunctional long- and short-range functional connectivity in the dyslexic

157 children (Vourkas et al., 2011). Another graph analysis from the same group of MEG data

158 obtained during rest revealed less organized network configuration in dyslexic children

159 (Dimitriadis et al., 2013). The current study will extend these findings by focusing on resting

160 state EEG data and by performing a MST analysis on these data. The use of resting state data

161 should indicate functional network differences between the groups that are not related to task-

162 related strategies and that are indicative of the underlying architecture of oscillatory EEG

163 activity. MST analysis goes beyond more conventional network analysis as (i) it allows an

164 unbiased network representation; (ii) it provides a comparison between groups/conditions

165 that is normalized; and (iii) it integrates features of small-worldness (clustering/ path length)

166 and scale-freeness (hubs) (e.g., Tewarie et al., 2015).

167 Methods

168 Participants

169 Twenty-nine third-grade dyslexic children (Mean age = 8.46; SD= 0.40) were recruited from

170 a nation-wide center for dyslexia in the Netherlands.1 All dyslexic children had a percentile

171 score of 10 or lower on a standard reading test and they participated in the EEG recordings

172 before starting their treatment program at the center. A group of 15 third-grade, control

173 children (8.75 ± 0.31 years old) was recruited from several primary schools attended by

174 children with the same socio-demographical background as the dyslexic group (see Table 1

175 for group characteristics). They had no history of reading difficulties and had a percentile

176 score of 25 or higher on standard reading tests (see below). All participants were native

177 Dutch speakers, received two and a half years of formal reading instruction in primary

178 education. Children with below average IQ (IQ < 85 on a non-verbal IQ-test), uncorrected

179 sight problems, hearing loss, diagnosis of ADHD or other neurological or cognitive

180 impairments were excluded. The study was approved by the Ethical Review Board of the

181 University and all parents or caretakers signed informed consent before the children

182 participated.

183 Behavio ral measurements

1 The current participants are part of a larger sample of 62 children taking part in the EEG recordings. From the original data set, resting-state data was not available for 3 participants due to complications during recording. Moreover, data from 6 participants were excluded due to excessive artifacts. In the remaining data (N= 53), the inspection of individual peak frequencies in the average spectra indicated that for the majority of participants the peak frequency fell within the low alpha (8-10 Hz) and high alpha (10-13 Hz) range (see Spectral Power section). We discarded data from children with a peak frequency equal or lower than 8 Hz as this might bias subsequent analysis in the lower frequency bands. A total of 9 subjects were excluded; 5 dyslexics (N=29) and 4 controls (N = 15). Demographic characteristics and reading scores of the complete sample are included in Supplementary Appendix A.

184 A series of tests was used to assess the reading skills of the participants (Fraga Gonzalez

185 et al., 2015). The children took the tests at their school.

186 Word reading skills were measured using a Dutch version of the One-minute test (Een-

187 Minuut-Test, EMT; Van den Bos et al., 1999), a time-limited test consisting of a list of 116

188 unrelated words of increasing difficulty. The number of correctly read words within 1 minute

189 serves as reading fluency score. Text reading fluency was assessed also using a test

190 consisting of a coherent text of increasing difficulty. The children were asked to read the

191 story out loud within 1 minute (Schoolvaardigheidstoets Technisch Lezen; de Vos, 2007). In

192 addition, the 3DM battery of tests (test reliability information available in Dyslexia

193 Differential Diagnosis; 3DM, Blomert and Vaessen, 2009) was individually administered.

194 The scores of the following 3DM subtests were used. Word Reading task: contains visually

195 presented high-frequency words, low-frequency words and pseudowords. Accuracy (%

196 correct) and fluency (correct words in 1 minute) were measured. Rapid automatized naming

197 (RAN): blocks of letters or numbers are presented and items have to be read as fast and

198 accurately as possible. Fluency is the time in seconds needed to name a screen of 15 items.

199 Letter-speech sound (LSS) association tasks: consist of identification and discrimination

200 tasks. In the identification task an aurally presented speech sound has to be matched to one

201 out of four visually presented letters. In the discrimination task the child has to judge whether

202 the speech sound and letter on the screen are congruent or incongruent. Computerized

203 Spelling: words are aurally presented and visually displayed on screen with missing letters.

204 Participants have to select the missing letter out of four alternatives. For the last two subtests,

205 accuracy (% correct) as well as response time (sec/item) is measured.

206 Finally, the RAVEN Coloured Progressive Matrices was used to obtain an estimate of

207 fluid IQ (RAVEN CPM; Raven et al., 1998) and the Child Behavior Checklist (CBCL) was

208 completed by the parents to exclude any additional behavioral problems (Achenbach et al.,

209 2008).

210 Procedure and equipment

211 EEG recordings were taken within a period of around 4 months and took place in a video-

212 controlled, dimly lit and air conditioned laboratory room. The participant and a lab assistant

213 were together at all times in the room while the experimenter controlling the recording was in

214 an adjacent room. The 2 minutes eyes-closed resting-state baseline was recorded at the

215 beginning of a longer experimental session (around 2 hours long, including visual and

216 audiovisual tasks). Children were instructed to keep their eyes closed and, when ready, to

217 make a button press to initiate the eyes-closed resting state EEG recording. Participants were

218 monitored at all times to ensure they complied to the instructions during the baseline

219 recording and that children did not show behavioral indications of drowsiness or sleep onset

220 during the recording.

221 EEG recording and signal processing

222 The EEG data were collected using a 64 channels Biosemi ActiveTwo system (Biosemi,

223 Amsterdam, Netherlands). EEG was recorded DC (low-pass: 5th order sync digital filter)

224 with a 1024 Hz sample rate. The Biosemi system uses two additional electrodes (Common

225 Mode Sense [CMS] and Driven Right Leg [DRL]) creating a feedback loop to replace the

226 conventional ground electrode (see for details). The

227 CMS electrode served as online reference. The 64 electrodes were distributed on the scalp

228 according to the 10-20 International system and applied using an elastic electrode cap

229 (Electro-cap International Inc.). Six external Flat-Type Active electrodes were used; four

230 electrodes for recording the vertical and horizontal electro-oculogram (EOG) and two

231 electrodes were placed at mastoids for off-line reference.

232 Continuous EEG data were imported in EEGLAB v. (Delorme and Makeig,

233 2004), an open source toolbox for Matlab (Mathworks, Inc.), using the averaged mastoids as

234 initial off-line reference. A two minutes long epoch was selected, time-locked to the button

235 press indicating the start of the eyes-closed resting-state recording.

236 The 2 min EEG epoch was imported in Brain Vision Analyzer (Version, ©

237 Brain Products) for further preprocessing. After importing, spline interpolation was applied to

238 channels with excessive artifacts. In the control group, interpolation was applied to data from

239 10 subjects (a maximum of 5 electrodes in one subject); in the dyslexic group interpolation

240 was applied to data from 8 subjects (a maximum of 5 electrodes in one subject). Data were

241 segmented in 30 epochs of 4 s (4096 sample points per epoch). The epochs were visually

242 inspected for eye blinks or muscle artifacts. For each subject 10 artifact-free epochs were

243 selected and exported to ASCII files.

244 The artifact-free epochs of 4 s were imported in Brainwave v0.9.117 (developed by C.S.;

245 freely available at where data were re-

246 referenced to the average of all scalp channels before performing spectral power analysis,

247 functional connectivity and MST metrics.

248 For the analysis of connectivity strength (measured with phase lag index; see Functional

249 Connectivity section), besides mean connectivity, the following sub-averages were

250 calculated: frontal (including the electrodes Fp1, Fp2, AF3, AF4, AF7, AF8, F1, F2, F3, F4,

251 F5, F6, F7 and F8); central (including the electrodes FC1, FC2, FC3, FC4, FC5, FC6, C1, C2,

252 C3, C4, C5, C6, CP1, CP2, CP3, CP4, CP5 and CP6); temporal (including the electrodes

253 FT7, FT8, T7, T8, TP7 and TP8) and parietal-occipital (including the electrodes O1, O2,

254 PO3, PO4, PO7, PO8, P1, P2, P3, P4, P5, P6, P7, P8, P9 and P10). The mean connectivity

255 between the electrodes included in each sub-average was calculated. These sub-averages

256 were chosen to examine strength of both short-range and long-range connectivity across

257 broad cortical regions that previous studies have found relevant to reading and dyslexia. Note

258 that the graph measures, which are the main focus of the present analysis, were derived from

259 the complete connectivity matrix including the 64 scalp electrodes.

260 Spectral power

261 Spectral power was calculated for all EEG channels using Fast Fourier Transformation

262 (FFT) in Brainwave, with a frequency resolution of 1 / 4 s = 0.25 Hz. The relative power

263 values were calculated for the following frequency bands: delta (0.5-4 Hz), theta (4-8 Hz),

264 alpha (8-13 Hz), beta (13-30 Hz) and gamma (30-48 Hz). The broad alpha range was used

265 instead of the lower alpha (8-10 Hz) and upper alpha (10-13 Hz) as some participants showed

266 an average peak frequency within the upper alpha range. Power values were averaged over

267 epochs.

268 Functional connectivity

269 The Phase Lag Index (PLI) was used to calculate functional connectivity between all 64

270 electrodes for each frequency band and in each segment, separately. The PLI measures phase

271 synchronization based on the asymmetry of the distribution of instantaneous phase

272 differences between two signals, which is determined using the analytical signal based on the

273 Hilbert transformation (Stam et al., 2007). The PLI is less sensitive to common sources since

274 the zero-lag synchronization is removed from the analysis (Porz et al., 2014). Furthermore,

275 the PLI quantifies the relative phase distribution's asymmetry; that is, that the likelihood that

276 the phase difference Ap will be in the interval - n < Ap < 0 is different from the likelihood

277 that it will be in the interval 0 < Ap < n. This implies the presence of a consistent, nonzero

278 phase difference ('lag') between two time series. The distribution is expected to be

279 symmetric if there is no coupling or if the median phase difference is equal to or centers

280 around a value of 0 mod n. The PLI is obtained from time series of phase differences Ap (tk),

281 k=1...N by means of:

282 PLI = l<sign[sin(Ap(tk))]>l

283 Here sign is the signum function. The PLI ranges between 0 and 1. A PLI of zero

284 indicates either no coupling or coupling with a phase difference centered around 0 (mod n).

285 A PLI of 1 indicates perfect phase locking at a value of Ap different from 0 (mod n). The

286 stronger this nonzero phase locking is, the larger PLI will be.

287 Minimum Spanning Tree

288 The Minimum Spanning Tree (MST) sub-graph was calculated for each PLI matrix

289 derived per segment. A schematic of the analytic steps is shown in Fig. 1. The MST is a

290 unique sub-graph based on a weighted matrix that connects all nodes of the network but does

291 not contain circles or loops. The MST always contains m = N-1 links, where N is the number

292 of nodes. The MST was constructed by applying Kruskal's algorithm (Kruskal, 1956). This

293 algorithm orders the distance of all links in an ascending order followed by the construction

294 of the MST with the link of the shortest distance, and then adding the following shortest

295 dis

tance link until all nodes are connected in a loop-less sub-graph. If adding a new link

296 results in the formation of a cycle, this link is skipped. In the current case, we use a maximum

297 spanning tree, which is equivalent to an MST based upon 1-PLI, which represents the sub-

298 network with maximum connectivity.

299 ................................................................

300 Insert Figure 1 about here

301 ................................................................

302 MST metrics provides information about the topological properties of the tree

303 following tree measures were used in this study: Degree, leaf number, betweenness centrality

304 (BC), eccentricity, diameter, hierarchy (Th), and degree correlation (R). The measures are

305 summarized in Table 2 and examples of tree topologies with increasing leaf number are

306 presented in Fig. 2 (a detailed description in Stam et al., 2014). The degree of a node is its

307 number of connections (edges), and the leaf fraction (L) represents the number of nodes on

308 the tree with degree = 1. The leaf number has a lower bound of 2 and upper bound of N -1.

309 The leaf number presents an upper bound to the diameter of the MST, which is the largest

310 distance between any two nodes of the tree. The upper limit of the diameter is d = m- L + 2,

311 which implies that the largest possible diameter will decrease with the increasing leaf

312 number. Eccentricity of a node is defined as the longest distance between that node and any

313 other node and is low if this node is central in the tree. The BC of a node u is the number of

314 shortest paths between any pair of nodes i and j that are running through u, divided by the

315 total number of paths between i and j. The BC value ranges between 0 and 1 since it is a

316 fraction. The BC relates to the importance of a node within the network. The nodes with the

317 highest BC have the highest load. For instance, in a star-like tree, the central node has a BC

318 of 1 and it could be easily overloaded, while the leaf nodes have a BC of 0. Degree,

319 eccentricity and BC are different measures for relative nodal importance and may indicate the

320 critical nodes in a tree.

322 Insert Figure 2 about here

323 .................................................

324 For a tree topology to result in optimal network performance, it should conform to two

325 criteria. Firstly, efficient communication would require a small diameter. Secondly, the tre(

326 topology would require preventing overload of hub nodes by setting a maximal BC max for

327 any tree node. The balance between these two criteria is reflected by the tree hierarchy (Th)

328 measure (Boersma et al., 2013), which is defined as:

2 ^B C^ax

or is mu

329 To assure Th ranges between 0 and 1, the denominator is multiplied by 2. If L = 2 (line-

330 like topology), and m approaches infinity, then Th approaches 0. If L = m (star-like

331 topography), then Th approaches 0.5. For leaf numbers in between these extreme values, Th

332 has higher values.

333 Finally, the degree correlation is an index of whether the degree of a node is correlated

334 with the degree of its neighboring vertices to which it is connected. A positive degree

335 correlation indicates that the graph is assortative; if the degree correlation is negative the

336 graph is called disassortative. The degree correlations can be quantified by computing the

337 Pearson correlation coefficient of the degrees of pairs of nodes connected by an edge.

338 Interestingly, most social networks tend to be assortative, while most technological and

339 biological networks tend to be disassortative (Newman, 2003).

340 Statistical analysis

341 One-way ANOVAs were used for group comparisons in behavioral measures, relative

342 power, PLI averages and MST measures. As indicated above, PLI and MST were calculated

343 per segment and then averaged for each participant. Prior to analysis, the PLI and MST

344 measures were transformed to their natural logarithm, y=ln (x), to obtain normal

345 distributions. For the behavioral analyses, standardized scores were used instead of raw

346 scores, in order to assess the child's position within the distribution of a normative sample.

347 Due to reduced variance, no reliable norm scores were available for the accuracy measures of

348 the three subtasks of the 3DM word reading; thus raw scores were used for these measures.

349 Additionally, for the MST measures, Bonferroni correction for multiple comparisons was

350 applied to p values for each frequency band. Finally, to examine the relation between tree-

351 derived measures and reading, regression analysis was performed in dyslexics and controls

352 separately for the MST measures in which we found group differences and the main reading

353 scores.

354 The same set of analyses was performed on the data of a sub-sample of 15 randomly

355 selected dyslexics to evaluate whether different sample sizes dyslexic children (n=29) and

356 controls (n=15) had any effect in the group differences. The main pattern of results reported

357 below did not change and it is presented in Supplementary Appendix B.

is preser /

suits of the

358 Results

359 Behavior

360 The results of the ANOVAs for reading accuracy and speed measures are shown in Table

361 1. The tat le shows a deficit in dyslexics that is mainly manifested by substantial differences

362 in the reading fluency measures. The dyslexic group attained reasonably high levels of

363 accuracy, although significantly lower than those of the control group. With regard to the

364 letter-speech sound measures, only the fluency scores were sensitive to group differences.

365 Spectral power and functional connectivity

366 The power spectra averaged across all electrodes for each group are shown in Fig. 3.

367 Controls and dyslexics both showed prominent peak frequencies in the alpha band, which did

368 not differ between groups. The ANOVAs performed on the relative power values in each

369 frequency band revealed no significant differences (in the total average or regional sub-

370 averages) between groups. For each frequency band outliers and extreme values in relative

371 power were detected and excluded for the subsequent analyses of connectivity and graph

372 measures. Outliers and extreme values were defined based on 1.5 inter-quartile range steps.

373 Accordingly, for the theta band 2 subjects from the dyslexic group were excluded (N = 27).

374 For the alpha band 1 subject from the dyslexic group was excluded (N= 28). No outliers or

375 extreme values were detected in the delta, beta or gamma band.

376 ................................................................

377 Insert Figure 3 about here

378 ................................................................

379 The PLI total values and sub-averages were calculated for each frequency band. The

380 ANOVAs yielded no significant differences in functional connectivity (total network or sub-

381 networks) between groups (all p's >.05). The total PLI values for each frequency band are

382 presented in Tables 3 and 4.

383 MST analysis

384 MST analysis yielded significant between group effects in the theta band (see Table 3 and

385 Fig. 4). Leaf fraction, reflecting the integration of information within the network, was

386 significantly lower in dyslexics relative to typical readers, F (1, 40) = 10.24, p = .003, n =

387 0.20. The group effect on diameter, representing the efficiency of communication between

388 the nodes, was significant also, F (1, 40) = 4.27, p = .045, n2 = 0.10, indicating higher

389 diameter in dyslexics relative to controls. The group effect on eccentricity, relating to node

390 centrality, just fell short of significance, F (1, 40) = 3.47, p = .070, n2 = 0.08, suggesting a

391 trend for higher eccentricity in dyslexics compared to controls. These group differences are

392 displayed in Fig. 5. Collectively these results indicate a less integrated network organization

393 in dyslexic children compared to controls.

394 ...................................................

395 Insert Figure 4 and 5 about here



397 For the alpha band, the group effects on diameter and eccentricity just failed to reach

398 significance, p = .080 and p = .098, respectively, suggesting trends for higher diameter and

399 eccentricity in dyslexics relative to controls2. Finally, for the gamma band, the ANOVA

400 revealed a somewhat higher hierarchy in controls relative to the dyslexic children but this

401 effect just failed to reach significance, F (1, 40) = 3.89, p = .055, n2 = 0.09. Group effects in

402 all other measures and frequency bands were not significant, ps > .124. Moreover, there were

403 no significant correlations between MST measures and reading performance.

405 The present study examined the topological characteristics of brain networks in dyslexics

406 and controls by applying MST analysis to eyes-closed resting state EEG. The present results

407 suggest that compared to controls, dyslexics may present differences in the way spontaneous

408 oscillato ry activity is o rganized . Our results showed a clear dissociation between PLI

2 In a control analysis including peak frequency as a covariate the main results in the theta band for leaf number remained significant (F = 9.94, p = .003, n2 = 0.20), while for the metric of diameter the group difference just fell short of significance (F = 4.07, p = .051, n2 = 0.09). Moreover, we performed additional analysis in the separate alpha 1 (8-10 Hz) and alpha 2 (10-13 Hz) frequency bands, similarly to other studies (e.g. Tewarie et al., 2014, Van Diessen et al., 2014). The group comparison in the alpha1 band revealed a significant effect in leaf number (F = 5.57, p = .023, n2 = 0.12), indicating a lower leaf number in dyslexics relative to control readers. No significant group effects were found in the other metrics. In the alpha2 band, we did not find significant group differences for any of the MST metrics analyzed.

404 Discussion

409 connectivity analyses vs. MST analyses of global network organization. That is, the PLI

410 analyses failed to reveal differences in connectivity strength between groups whereas the

411 MST analyses yielded between groups differences in network organization as revealed in the

412 theta band. The MST method should correct for potential bias in comparing networks (Stam

413 et al., 2014). Our pattern of findings presents another illustration of the differences between

414 connectivity vs. network analysis of EEG data (see also Stam and van Straaten, 2012). More

415 specifically, the MST analysis showed for dyslexic children a smaller leaf fraction indicating

416 less network integration compared to controls. In addition, there was a significant group

417 difference for diameter suggesting less communication between nodes of the network in

418 dyslexics compared to controls. In terms of the extreme tree topologies, the current pattern of

419 results suggests a more path-like configuration in dyslexic children and a more star-like

420 ,opology in ,ypically reading chlldren (see Flg. 4)-

421 The current group difference in network topology is indicative of a less integrated

422 network configuration in dyslexic children compared to controls (Olde Dubbelink et al.,

423 2014; Stam et al., 2014). This finding is in accordance with previous functional connectivity

424 studies suggesting a disrupted network structure and mixed patterns of connectivity

425 abnormalities in dyslexia (Frye et al., 2012; Koyama et al., 2013). A relevant consideration

426 when interpreting the current results is the relation between MST measures and more

427 conventional graph metrics pertaining to network models such as small-world and scale-free

428 networks. Tewari et al. (2015) examined this relation by performing an extensive and

429 sys tematic series of simulation studies. We observed for dyslexic children a lower leaf

430 fraction and a trend for higher diameter relative to controls. Tewarie et al., (2015) observed

431 that these two measures are strongly related to path length. MST leaf was negatively related

432 to path length. More specifically, MST leaf was low for trees derived from regular networks

433 and increased as these networks became more random. MST diameter, on the other hand, was

434 positively related to path length. That is, diameter increased as networks became more

435 regular. This finding is consistent with a recent study that examined the topology of structural

436 networks in Chinese dyslexics in which a longer path length was observed for dyslexics

437 relative to controls (Liu et al., 2015). Interestingly, in the Tewari et al. (2015) simulation

438 study, MST leaf fraction and diameter were also strongly related to the 'scale freeness' of the

439 network. In particular, leaf fraction increased from regular to random networks and it was

440 much larger for scale-free networks. Accordingly, the current results may also indicate a

441 deviation from scale-free topologies that is larger in dyslexics compared to controls. A scale-

442 free topology is indicative of the presence of highly connected hub nodes in the network

443 (Stam, 2014). In this regard, the current findings may suggest dysfunctional hub nodes in

444 dyslexia.

445 It should be emphasized that the main group differences in network organization were

446 found in the theta band. The present results are consistent with previous research on

447 functional and scaling aspects of oscillatory activity. Regarding general properties of the

448 brain as an oscillatory system, research suggests that slow oscillations such as theta recruit

449 large networks whereas higher frequencies are more confined to smaller networks (Buzsaki

450 and Draguhn, 2004). Further, it is proposed that synchronous activity of lower frequency

451 bands such as theta, mediate long range integration between processes involving several

452 cortical areas (von Stein and Sarnthein, 2000). More specifically, theta frequencies have been

453 related to long range interactions during top-down processes such as working memory

454 retention (von Stein and Sarnthein, 2000). In relation language-specific functions, it has been

455 suggested that synchronous theta activity may play an important role in speech processing

456 (Luo and Poeppel, 2007; Poeppel et al., 2008) and language comprehension (Bastiaansen et

457 al., 2008). Finally, the findings of current study support previous evidence suggesting

458 abnormalities in theta oscillations associated with reading difficulties (Arns and Peters, 2007;

459 Goswami, 2011; Klimesch, 1999; Marosi et al., 1995; Spironelli et al., 2008). Previous

460 reports of theta band abnormalities in dyslexics or poor readers relative to controls include

461 atypical lateralization in several reading tasks (Spironelli et al., 2008), increased power in

462 frontal and temporal regions at rest (Arns and Peters, 2007), higher coherence (Marosi et al.,

463 1995) and deficits in temporal sampling of phonological information (see review in

464 Goswami, 2011). The current results extend previous findings linking abnormalities in the

465 theta band to reading impaired groups by showing a less integrated network configuration in

466 dyslexics' theta spontaneous oscillatory activity.

467 The current results showed also a between-group effect in the gamma band that just fell

468 short of significance. The dyslexic children showed a lower tree hierarchy than controls. It

469 should be noted, however, that the gamma band in scalp EEG recordings may be strongly

470 affected by muscle artifact (Whitham et al., 2007). Consequently, a previous study using

471 graph analysis excluded the higher frequency gamma band from analysis (Lee et al., 2010).

472 In this regard, we hesitate to interpret the current findings for the gamma band, the more so

473 because we are dealing with child data that are typically more affected by muscle artifact

474 compared to adult participants.

475 It should be noted that the current study defined a broad alpha band (see Spectral Power).

476 Previously, it has been suggested that lower and upper frequency alpha bands may be

477 involved in different cognitive processes (see a review of some of these issues in van Diessen

478 et al., 2015). In addition, individual peak frequency varies with age and state of wakefulness

479 (Klimesch, 1999). Given the current scope and focus on resting-state and graph metrics, we

480 opted for a broad alpha band definition to avoid biases from individual peak variability.

481 Future studies could systematically investigate these issues and provide a more detailed

482 description of the cognitive processes associated with the frequency bands in which network

483 metrics are calculated.

484 The MST metrics of the EEG obtained during rest did not relate to the reading measures

485 differentiating children with dyslexia from controls. Previously, Dimitriades et al., (2013) did

486 observe a positive relation between local efficiency of temporo-parietal networks in the beta

487 band of the resting-state EEG and word reading measures in children with reading difficulties

488 but not in typical controls. Similarly, Vourkas et al. (2011) reported significant correlations

489 between graph metrics and phonological decoding ability but this relation was obtained for

490 task-related EEG. In view of the limited studies available to date we are reluctant to interpret

491 the current absence of a relation between reading ability measures and MST metrics. Future

492 studies should examine the potential relations between these measures more systematically

493 by comparing both resting-state and task-related EEG measures.

494 There are a few limitations to the current study. First, the current study used a modestly

495 sized EEG montage (64 electrodes). Although MST metrics are not affected by connectivity

496 strength and network density, some measures are sensitive to network size. Thus, our results

497 should be replicated by using a high-density electrodes array, or preferably MEG source

498 space networks, to assess relative nodal importance in network performance. Secondly,

499 although PLI is more robust than other connectivity measures to methodological problems

500 such as volume conduction (Stam et al., 2007), it is yet unclear how interpolation may affect

501 connectivity measures. At some instances we had to resort to interpolation and the potential

502 effects of interpolation should be examined more systematically. The current assessment of

503 this issue suggests that, in view of the limited number of interpolations, it seems unlikely that

504 interpolation impacted the connectivity weights. Moreover, a control analysis including only

505 participants without interpolated data continued to show the between-groups effect on leaf

506 number. The results of the control analysis are reported in Supplementary Appendix C.

507 Further, in the current study, the PLI sub-averages differed in the number of electrodes and

508 we cannot exclude the possibility that between-group differences in signal-to noise ratio

509 might have affected our MST metrics. It should be noted, however, that the Tewarie et al.

510 (2015) simulation studies indicated that the MST metrics are quite robust to noise. Finally,

511 another potential limitation relates to the stability of our network measures. The current

512 selection of segments was constrained by a relatively short baseline recording (2 minutes)

513 and the presence of artifacts which are common in children EEG resting-state data. Because

514 of this, we could not perform additional analyses on the effects of various epoch length in our

515 graph and connectivity strength metrics. Importantly, however, these issues were

516 systematically examined in a recent study suggesting that MST metrics derived from PLI are

517 almost unaffected by epoch length and produce stable results also for short epochs (Fraschini

518 et al., 2016). Those results suggest an advantage of tree-derived metrics when comparing

519 results across studies in contrast with traditional graph metrics.

520 Conclusion

521 In conclusion, the global organization of functional brain networks may be compromised

522 in dyslexics. The current MST analysis indicated a more path-like topology in dyslexics

523 compared to controls for the EEG theta band. This finding suggests a less integrated network

524 configuration in dyslexia. More specifically, the current results might indicate less efficient

525 long

-range connections in dyslexics, which would be in line with evidence suggesting

526 disrupted connectivity between the distant cortical areas of the reading network (Sandak et

527 al., 2004). The current findings also extend previous evidence suggesting abnormalities in

528 connectivity across multiple brain networks beyond the reading network in dyslexics (Finn et

529 al., 2014). The notion that dyslexics may present differences in widespread topology of brain

530 connectivity would be compatible with evidence and theoretical approaches suggesting

531 deficits in general sensory and attentional functions (e.g. visuospatial attention, visual

532 attention span, auditory processing, etc.). Importantly, MST metrics could help characterizing

533 the heterogeneity within dyslexia, as different underlying deficits may result in similar

534 reading impairments. Future studies employing MST analysis might want to adopt a

535 longitudinal perspective in examining the developmental trajectories of network organization

536 during reading acquisition. Furthermore, it would be of considerable interest to examine how

537 functional network organization is changed following reading intervention (e.g., Koyama et

538 al., 2013).

540 Conflict of interest

541 None of the authors have potential conflicts of interest to be disclosed.

543 Acknowledgements

544 We dedicate this paper to our co-author professor Leo Blomert. His contributions to the

545 initial stages of the project prior to his untimely death were significant. This project is part of

546 the research program "Fluent reading neurocognitively decomposed: The case of dyslexia -

547 HCMI 10-59" funded by the Netherlands Initiative Brain and Cognition, a part of the

548 Organization for Scientific Research (NWO) under grant number 056-14-015. The funders

549 had no role in study design, data collection and analysis, decision to publish, or preparation

550 of this manuscript.

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751 connectivity and reading abilities in first and second languages. NeuroImage, 84, 546752 53. doi:10.1016/j. neuroimage.2013.09.006

754 Figure Legends

755 Fig. 1. Schematic of the graph analysis. First, artifact-free epochs are filtered for each

756 frequency band (A). Secondly, the functional connectivity matrix based on Phase Lag Index

757 (PLI) is calculated for each frequency band and epoch (B). Finally, the Kruskal's algorithm is

758 applied to obtain the Minimum Spanning Tree (MST) matrix (C-left); the resulting loopless

759 graph is displayed on a scalp projection (C-middle) and as a tree (C-right). The tree view

760 shows the hierarchical structure of the graph starting from an arbitrary root node (in this case

761 FP1), the color map of the nodes from blue to red represents lower to higher betweenness

762 centrality. For illustrative purposes this figure shows the MST obtained from the PLI matrix

763 averaged across epochs and subjects of the control group (N=15).

764 Fig. 2. Examples of trees for increasing leaf number including the two extreme forms of

765 trees. All of them have 14 nodes (circles) and 13 edges (lines). On the left a line-like tree

766 with the lowest possible leaf number which is 2. The middle example shows a tree

767 configuration with eight leaf nodes. On the right, a star-like tree with the highest possible leaf

768 number which equals the number of edges.

769 Fig. 3. Power spectra averaged across 64 EEG scalp channels for the control and the

770 dyslexic group.

771 Fig. 4. MST matrices (left panels) and MST graph in scalp view (center panel) and tree

772 view (right panel) for the theta band for controls (above) and dyslexics (below). For 73 illustra

774 Fig. 5. (A) Group averages for leaf fraction, (B) eccentricity and diameter measures of the

773 illustrative purposes the MST algorithm was performed on the averaged PLI matrices.

775 MST. Open bars refer to controls and filled bars to dyslexics. * p < 0.05.


Table 1.

Sample characteristics and descriptive statistics showing reading accuracy and fluency scores.

Controls M(SD)

Sex ratio (m:f) Handedness (L:R)* Age

RAVEN - IQ test a

3DM Word reading - accuracy b High Frequency Low Frequency Pseudo Total [T]c

3DM Word reading - fluency [T] High Frequency Low Frequency Pseudo Total

One-Minute Test -fluency [SS]d Text Reading - fluency [T]**

3DM Spelling - accuracy[T] 3DM Spelling - fluency[T]

3DM Phoneme deletion - accuracy [T]**

Letter-speech sound associations [T]

L-SS identificacion - accuracy

iscrimination - accuracy L-SS identificacion - fluency L-SS discrimination - fluency**

ÖSS dis


3DM Naming speed scores[T] Letters numbers Total

15 6:9 2:10 8.75 (0.31) 6.70 (1.51)

Dyslexies M(SD)


29 16:13 2:27 8.96 (0.40) 7.11 (1.51)

0.07 0.02

99.28 (1.05) 93.10 (5.93) .000 0.27

98.32 (2.54) 86.31 (14.48) .003 0.19

88.70 (8.48) 73.33 (17.43) .003 0.20

51.40 (8.00) 33.72 (12.58) .000 0.37

54.27 (7.58) 31.38 (6.14) .000 0.74

56.80 (8.98) 32.07 (6.46) .000 0.72

54.93 (9.71) 30.93 (6.37) .000 0.70

55.93 (9.51) 31.00 (5.40) .000 0.75

12.07 (2.94) 3.97 (1.97) .000 0.74

55.27 (8.41) 33.21 (6.30) .000 0.70

51.73 (8.62) 36.21 (6.70) .000 0.51

54.33 (9.90) 36.55 (6.01) .000 0.57

53.73 (8.39) 39.61 (8.32) .000 0.41

46.87 (8.65) 43.34 (12.99) .350 0.02

50.80 (10.28) 44.43 (9.63) .050 0.09

51.53 (7.67) 41.79 (6.97) .000 0.30

51.73 (7.36) 45.46 (8.95) .025 0.12

50.93 (6.95) 36.57 (8.05) .000 0.45

52.73 (10.67) 36.21 (8.50) .000 0.43

50.80 (7.73) 35.54 (9.15) .000 0.42

a C scores (M = 5, SD = 2).b Raw scores. c T scores (M = 50, SD = 10). d SS scores (M = 10, SD= 3) *Data missing for 3 participants; Typical N = 12. ** Data missing for one participant; Dyslexics N = 28.

Table 2.

MST measures summary.


Leaf fraction



BC Betweenness Centrality k Kappa Th Tree Hierarchy

R Degree correlation

Number of nodes in MST Number of links in the MST Number of neighbors for a given node in the MST Fraction of nodes with degree = 1 (leafs) in the MST. Largest distance between any two nodes of the tree. Longest distance between a reference node and any other node

Fraction of all shortest paths that pass through a particular node

Measure of the broadness of the degree distribution (degree divergence)

A hierarchical metric that quantifies the trade-off between large scale integration in the MST and the overload of central nodes

Correlation between the degrees of a node and the degree of the neighboring vertices to which it is connected

Table 3.

PLI average and MST measures.

Typical (N = 15) M SD

Dyslexies (N =29 ) M SD

p value n 2

Delta PLI

Degree Leaf

Eccentricity Kappa Diameter BC

Degree Correlation Hierarchy

Thetaa PLI

Degree Leaf

Eccentricity Kappa Diameter BC

Degree Correlation Hierarchy

Alphab PLI

Degree Leaf

Eccentricity Kappa Diameter BC

Degree Correlation Hier

0.202 0.163 0.583 0.168 3.551 0.216 0.704 -0.325 0.418

0.176 0.152 0.584 0.169 3.415 0.216 0.701 -0.327 0.419

0.209 0.187

0.197 0.713 -0.345 0.441

(0.012) (0.022) (0.012) (0.010) (0.259) (0.013) (0.026) (0.030) (0.015)

(0.008) (0.011) (0.013) (0.011) (0.149) (0.015) (0.022) (0.037) (0.015)

(0.033) (0.028) (0.030) (0.013) (0.398) (0.018) (0.025) (0.028) (0.018)

0.207 0.160 0.576 0.170 3.501 0.219 0.698 -0.321 0.417

0.174 0.148 0.569 0.174 3.341

0.696 -0.319 0.412

0.200 0.185 0.609 0.160 3.892 0.206 0.712 -0.352 0.432

(0.013) (0.022) (0.020) (0.011) (0.270) (0.014) (0.033) (0.039) (0.023)

(0.0 (0.015)

(0.015) (0.008) (0.165) (0.011)

(0.023) (0.031) (0.016)

(0.037) (0.033) (0.027) (0.011) (0.466) (0.015) (0.032) (0.038) (0.024)

1.94 0.31 1.37 0.36 0.37 0.33 0.


0.70 0.86

3.47 2.14 4.27 0.49 0.55 2.13

0.68 0.11 2.59 2.86 0.37 3.22 0.03 0.29 1.74

.171 .580 .248 .552 .543 .568 .577 .643 .865

.408 .359

.003* .070 .151

.489 .463 .152

.413 .744 .115

.098 .545 .080 .862 .593 .194

0.04 0.01 0.03 0.01 0.01 0.01 0.01 0.00 0.00

0.02 0.02

0.08 0.05

0.01 0.01 0.05

0.02 0.00 0.06 0.07 0.01 0.07 0.00 0.01 0.04

text represents significant results (p < 0.05 ); italic text represents results at trend level; Significant after Bonferroni correction at p = 0.059 (i.e., p < 0.006).

Notes. Bold tex

a Two outliers based on spectral power excluded; Dyslexies N = 27.b One outlier based on spectral power excluded; Dyslexies N = 28. MST, minimum spanning tree; PLI, phase lag index; BC, betweenness centrality.

Table 4.

PLI average and MST measures.

Typical (N = 15)

Dyslexics (N =29 )

M SD M SD F p value n 2

PLI 0.099 (0.006) 0.101 (0.010) 0.43 .514 0.01

Degree 0.160 (0.019) 0.162 (0.019) 0.09 .770 0.00

Leaf 0.582 (0.018) 0.580 (0.022) 0.07 .796 0.00

Eccentricity 0.168 (0.010) 0.168 (0.009) 0.00 .958 0.00

Kappa 3.516 (0.244) 3.542 (0.275) 0.08 .773 0.00

Diameter 0.216 (0.013) 0.216 (0.012) 0.06 .811 0.00

BC 0.691 (0.026) 0.702 (0.021) 2.28 .138 0.05

Degree Correlation -0.319 (0.027) -0.316 (0.040) 0.18 .675 0.00

Hierarchy 0.425 (0.015) 0.417 (0.020) 1.72 .197 0.04

PLI 0.092 (0.006) 0.091 (0.006) 0.04 .840 0.00

Degree 0.224 (0.041) 0.214 (0.061) 0.69 .410 0.02

Leaf 0.637 (0.034) 0.621 (0.038) 2.04 .160 0.05

Eccentricity 0.152 (0.011) 0.158 (0.015) 2.02 .162 0.05

Kappa 4.587 (0.875) 4.468 (1.381) 0.41 .528 0.01

Diameter 0.196 (0.014) 0.205 (0.019) 2.31 .136 0.05

BC 0.725 (0.027) 0.725 (0.032) 0.00 .942 0.00

Degree Correlation -0.366 %0.031) -0.356 (0.040) 0.89 .350 0.02

Hierarchy 0.443 (0.020) 0.431 (0.016) 3.89 .055 0.09

Notes. Bold text represents significant results ( p < 0.05 ); italic text represents results at trend level; MST, minimum spanning tree; PLI, phase lag index; BC, betweenness centrality.

Control (N = 15)

Dyslexies (N = 27)

PLI MST matrix MST graph