## 4 Results and Discussions
### Hub Identification  
A cartographic system with the statistical thresholds of 25 th and 75 th percentiles for both distributions of \(PC\) and \(z\) was used to identify the hub regions. As an example, in Figure 7 nine sectors of the resulting partitions are shown for the SYNC network related to the first session of the subject together with the distributions of the two topological metrics. The hub regions are confined in the upper part of the plane. In details, kinless hubs, associated with more modules, are localized in the upper right, peripheral hubs with most of the connections within their own module are localized in the upper left side, while the other connector hubs are identified as between these two extreme categories. Figure 6: The functional modules detected in SYNC networks (**top** panel), Pearson correlation network (**middle** panel) and coherence network (**bottom** panel). All the ROIs within the same module are indicated with spheres of the same color. In Table 1 is reported the complete list of all the regions identifies as hubs with their categories for the three functional networks. It is interesting to note that beyond the specific role designated to each hub in the three network configurations, in the Pearson's network many connector hubs are located in the temporal lobe, which instead show just two hubs in the SYNC network, while most of the hubs of the coherence are located in the frontal lobe. Several nodes we detected as connector hubs were also identified as integrative nodes in frontal, inferior parietal areas, cingulate and some regions of both default-mode and executive control networks in the adult brain [55; 56; 57]. In addition, in both SYNC and Pearson networks, the cerebellar crus regions are detected as important hubs, confirming the complex associations among the cerebellar regions and the cerebral cortex captured during the resting state by means of functional connectivity MRI [58]. Another interesting aspect concerns the presence of kinless hubs: such kind of nodes belong to any modules, hence they particularly facilitate the integration of information among the brain areas. These nodes are identified in the upper right side of the plane. However, in many works, advanced methodologies are proposed to identify functional connectivity hubs [59]. In this work, we explored an intuitive approach to depict central and influential nodes in functional connectivity networks. In general, hubs are identified by using consensus scores across several centrality metrics: the nodes with the highest scores on a set centrality measures are usually designated as hubs [60]. However, the level of influence of such nodes depends on the distribution of the metrics used to define hubness. As an example, if the distribution is long-tailed, the network contains a subset of outlier nodes that are considerably more central than others; therefore, they can be considered influential hubs [57]. Here, the range limits for the participation coefficient \(PC\) are defined by simple statistical thresholds, hence these ranges correspond to the extreme values assumed by the coefficient in both networks. Actually, in the literature, a strict definition of the kinless hub role corresponds to \(PC>0.7\). According to many studies, these nodes are almost completely absent in the cortex of primates [60]. As shown in Figure 8, we found lower values of the upper limit of PC in both Pearson and coherence networks in all the sessions, while the SYNC networks exhibit values of \(PC\) corresponding to the formal definition, effectively detecting the presence of highly versatile hub nodes. These results are confirmed in the connectivity analysis of another subject reported in the Supplementary Information file. Figure 7: Cartographic presentation of nodes classification in the SYNC network of the first session. The red lines indicate the 25 th and 75 th of the two distributions of \(PC\) and \(z\) selected as the statistical thresholds to perform the plane partitions.