## 3 Results
### Within-Group Comparison of Global SWP Measures of Functional Connectivity  
There were no statistically significant differences in network measures between boys with DD and girls with DD in both task conditions (Figure 2A,B; Tables S3 and S4). Figure 1: Reaction times (median, -; mean, *) of boys (blue) vs. girls (yellow) in the contrast illusion discrimination task: (**A**) boys with DD vs. girls with DD; (**B**) control boy vs. control girl. The stars above the violins indicate statistically significant differences, \(p<0.0001\). Control boys exhibited statistically higher \(\Delta\)C and smaller SWP (\(\phi\)) than control girls in low-contrast LSFI:  
(1) The \(\alpha\)-frequency network: \(\Delta\)C of the (\(\Delta\)C: \(\chi^{2}\) = 8.48; \(p\) = 0.001; Q = 0.48; Table S3);  
(2) the \(\beta\)2-frequency network: \(\phi\), \(\Delta\)C of only in the low-contrast (\(\phi\), \(\Delta\)C: \(\chi^{2}\) = 8.07; \(p\) < 0.005, Q = 0.6; Table S3). Sex differences were found in the high-contrast SLF at:  
(1) \(\beta\)-frequencies \(\phi\), \(\Delta\)C, \(\Delta\)L (\(\beta\)1: \(\phi\), \(\Delta\)C: \(\chi^{2}\) > 13.86 \(p\) = 0.002, Q > 0.58; \(\beta\)2: \  
related to language, auditory, motor, motion-sensitivity, and visual attentional processing (FT9-10, C3, C5, C2, CP2, PO4, P8; Figure S2); and for the girls with DD, in areas related to language processing, sensitivity to movement, and visual attention (FT9-10, P7, PO7, O1; ref. Figures S2 and S3). The hub distribution between boys and girls with DD was statistically different in the \(\gamma\)1-frequency network (according to hub strength; \(\chi^{2}\) = 7.26, \(p\) = 0.007, Q = 0.4; Table S5); as in girls with DD, it was in areas related to language processing, reading, motor, auditory processing, sensitivity to visual information and that to optic flow in the right hemisphere (Fz, FC4, C2, C4, C6, P4, O1), and in boys, in language processing, reading, motor, and auditory sub-networks in the left hemisphere (F7, F3, FC3, C3-C4, C5; ref. Figures S2 and S3). The hub distribution between the two DD sex groups was statistically different in the \(\beta\)1-frequency network, relative to hub strength, in the high-contrast illusion (\(\chi^{2}\) = 9.65, \(p\) = 0.001, Q = 0.3; Table S6): for boys with DD, in areas related to motor processing, language comprehension, expression, and reading (FC4, C4, CP4, P3, Pz, Oz); for the girls with DD, in more areas related to language comprehension, expression, reading, basic and complex auditory, visual motion processing, and visual attention, mostly in the left hemisphere (AF3, FC3, C3, CP1, CP3, T7, PO4, P7, O1; Figure 4). Figure 4: Frequency networks in boys with DD (first column; main hubs and strong connections in red color), girls with DD (second column), and mixed group with DD (girls and boys with DD, third column): (1) low-contrast LSF illusion: BC of hubs of \(\alpha\)-network (larger in boys: FT9-10, C3, C5, C2, CP2, PO4, P8; girls: FT9-10, P7, PO7, O1), and all DD: FT9-10, C2, C3, P7, O1; Strø of hubs of \(\gamma\)1-network (larger in girls: Fz, FC4, C2, C4, C6, P4, O1; boys: F3, FC3, F7, C3-C4, C5), all DD: FC3-4, C4, C5-6, CP3; (2) high-contrast LSF illusion: Strø of hubs in \(\beta\)1-network (larger Strø in boys: FC4, C4, CP4, P3, P2, Oz; girls: AF3, FC3, C3, CP1, T7, CP3, P7 O1, PO4), all DD (CP1, CP3, PO4, P2); and BC of the hubs of \(\beta\)1-network (larger in boys: FC4, FT10, T7, PO4, PO7, O2; girls: Fz, F7, CP3, T7, PO4 P7, PO7, O1), all DD (T7, PO4, PO7, P7; ref. Figure S2). In the \(\beta\)1-frequency network of boys and girls with DD, the hubs distributions with the greatest BC were statistically different (\(\chi^{2}\) = 8.37, \(p\) = 0.003, Q = 0.3; Table S6).