This article presents a new methodology for investigation of the organization of the overall and hemispheric brain network of patients with attention-deficit hyperactivity disorder (ADHD) using theoretical analysis of a weighted graph with the goal of discovering how the brain topology is affected in such patients. The synchronization measure used is the nonlinear fuzzy synchronization likelihood (FSL) developed by the authors recently. Recent evidence indicates a normal neocortex has a small-world (SW) network with a balance between local structure and global structure characteristics. Such a network results in optimal balance between segregation and integration which is essential for high synchronizabilty and fast information transmission in a complex network. The SW network is characterized by the coexistence of dense clustering of connections (C) and short path lengths (L) among the network units. The results of investigation of C show the local structure of functional left-hemisphere brain networks of ADHD diverges from that of non-ADHD which is recognizable in the delta electroencephalograph (EEG) sub-band. Also, the results of investigation for L show the global structure of functional left-hemisphere brain networks of ADHD diverges from that of non-ADHD which is observable in the delta EEG sub-band. It is concluded that the changes in left-hemisphere brain's structure of ADHD from that of the non-ADHD are so much that L and C can distinguish the ADHD brain from the non-ADHD brain in the delta EEG sub-band.
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