Brain Functional Network Topology in Autism Spectrum Disorder: A Novel Weighted Hierarchical Complexity Metric for Electroencephalogram.

Recent complex network analysis reflected the brain network as a modular network with small-world architecture in Autism Spectrum Disorder (ASD). Network hierarchy, which can provide important information to comment on brain networks, especially in ASD, has not yet been fully explored. The present work proposes a Weighted Hierarchical Complexity (WHC) metric to study network topology using the node degree concept. To do so, brain networks have been constructed using a visibility algorithm. To ensure proper mapping of network characteristics by the proposed metric, it is statistically compared to other network measures of brain connectivity related to integration, segregation and centrality. Further, for automated ASD classification, these network metrics were fed to explainable machine learning algorithms and the results revealed that brain regions tend to hierarchically coordinate in ASD, but the hierarchical architecture is attenuated after a few steps compared to networks in Typically Developing individuals (TDs). The value of WHC (0.55) reveals architecture up to three levels (four-degree nodes) with an abundance of 2-degree hubs in ASD indicating high intra-connectivity compared to TDs (WHC = 0.78; four-level spread). The explainable Support Vector Machine (SVM)-classifier model highlighted the role of WHC in classifying ASD with 98.76% of accuracy. The graph-theory metrics ensured that weaker long-range connections and stronger intra-connections are markers of ASD. Thus, it becomes evident that whole-brain architecture can be characterised by a chain-like hierarchical modular structure representing atypical brain topology as in ASD.