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Objective: To determine the functional connectivity of different EEG bands at the ''baseline'' situation (rest) and during mathematical thinking in children and young adults to study the maturation effect on brain networks at rest and during a cognitive task. Methods: Twenty children (8-12 years) and twenty students (21-26 years) were studied. The synchronization likelihood was used to evaluate the interregional synchronization of different EEG frequency bands in children and adults, at rest and during math. Then, graphs were constructed and characterized in terms of local structure (clustering coefficient) and overall integration (path length) and the ''optimal'' organization of the connectivity i.e., the small world network (SWN). Results: The main findings were: (i) Enhanced synchronization for theta band during math more prominent in adults. (ii) Decrease of the optimal SWN organization of the alpha2 band during math. (iii) The beta and especially gamma bands showed lower synchronization and signs of lower SWN organization in both situations in adults. Conclusion: There are interesting findings related to the two age groups and the two situations. The theta band showed higher synchronization during math in adults as a result of higher capacity of the working memory in this age group. The alpha2 band showed some SWN disorganization during math, a process analog to the known desynchronization. In adults, a dramatic reduction of the connections in gray matter occurs. Although this maturation process is probably related to higher efficiency, reduced connectivity is expressed by lower synchronization and lower mean values of the graph parameters in adults.

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