One major problem in neuroscience is the comparison of functional brain networks of different populations, e.g., distinguishing the networks of controls and patients. Traditional algorithms are based on search for isomorphism between networks, assuming that they are deterministic. However, biological networks present randomness that cannot be well modeled by those algorithms. For instance, functional brain networks of distinct subjects of the same population can be different due to individual characteristics. Moreover, networks of subjects from different populations can be generated through the same stochastic process. Thus, a better hypothesis is that networks are generated by random processes. In this case, subjects from the same group are samples from the same random process, whereas subjects from different groups are generated by distinct processes. Using this idea, we developed a statistical test called ANOGVA to test whether two or more populations of graphs are generated by the same random graph model. Our simulations' results demonstrate that we can precisely control the rate of false positives and that the test is powerful to discriminate random graphs generated by different models and parameters. The method also showed to be robust for unbalanced data. As an example, we applied ANOGVA to an fMRI dataset composed of controls and patients diagnosed with autism or Asperger. ANOGVA identified the cerebellar functional sub-network as statistically different between controls and autism (p < 0.001).

Recent studies have suggested abnormal brain network organization in subjects with Autism Spectrum Disorders (ASD). Here we applied spectral clustering algorithm, diverse centrality measures (betweenness (BC), clustering (CC), eigenvector (EC), and degree (DC)), and also the network entropy (NE) to identify brain sub-systems associated with ASD. We have found that BC increases in the following ASD clusters: in the somatomotor, default-mode, cerebellar, and fronto-parietal. On the other hand, CC, EC, and DC decrease in the somatomotor, default-mode, and cerebellar clusters. Additionally, NE decreases in ASD in the cerebellar cluster. These findings reinforce the hypothesis of under-connectivity in ASD and suggest that the difference in the network organization is more prominent in the cerebellar system. The cerebellar cluster presents reduced NE in ASD, which relates to a more regular organization of the networks. These results might be important to improve current understanding about the etiological processes and the development of potential tools supporting diagnosis and therapeutic interventions.

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