Application of graph theory to analysis of functional networks in the brain is an important research trend. Extensive research on the resting state has shown a "small-world" organization of the brain network as a whole. However, the small-worldness of children's brain networks in a working state has not yet been well characterized. In this paper, we used a custom-made, child-sized magnetoencephalography (MEG) device to collect data from children while they were watching cartoon videos. Network structures were analyzed and compared with scores on the Kaufman Assessment Battery for Children (K-ABC). The results of network analysis showed that (1) the small-world scalar showed a negative correlation with the simultaneous processing raw score, a measure of visual processing (Gv) ability, and (2) the children with higher simultaneous processing raw scores possessed network structures that can be more efficient for local information processing than children with lower scores. These results were compatible with previous studies on the adult working state. Additional results obtained from further analysis of the frontal and occipital lobes indicated that high cognitive performance could represent better local efficiency in task-related sub-networks. Under free viewing of cartoon videos, brain networks were no longer confined to their strongest small-world states; connections became clustered in local areas such as the frontal and occipital lobes, which might be a more useful configuration for handling visual processing tasks.
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