The application of graph analysis methods to the topological organization of brain connectivity has been a useful tool in the characterization of brain related disorders. However, the availability of tools, which enable researchers to investigate functional brain networks, is still a major challenge. Most of the studies evaluating brain images are based on centrality and segregation measurements of complex networks. In this study, we applied the concept of graph spectral entropy (GSE) to quantify the complexity in the organization of brain networks. In addition, to enhance interpretability, we also combined graph spectral clustering to investigate the topological organization of sub-network's modules. We illustrate the usefulness of the proposed approach by comparing brain networks between attention deficit hyperactivity disorder (ADHD) patients and the brain networks of typical developing (TD) controls. The main findings highlighted that GSE involving sub-networks comprising the areas mostly bilateral pre and post central cortex, superior temporal gyrus, and inferior frontal gyri were statistically different (p-value=0.002) between ADHD patients and TD controls. In the same conditions, the other conventional graph descriptors (betweenness centrality, clustering coefficient, and shortest path length) commonly used to identify connectivity abnormalities did not show statistical significant difference. We conclude that analysis of topological organization of brain sub-networks based on GSE can identify networks between brain regions previously unobserved to be in association with ADHD.
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