Our study used functional magnetic resonance imaging and fractal functional connectivity (FC) methods to analyze the brain networks of Autism Spectrum Disorder (ASD) and typically developing participants using data available on ABIDE databases. Blood-Oxygen-Level-Dependent time series were extracted from 236 regions of interest of cortical, subcortical, and cerebellar regions using Gordon’s, Harvard Oxford, and Diedrichsen atlases respectively. We computed the fractal FC matrices which resulted in 27,730 features, ranked using XGBoost feature ranking. Logistic regression classifiers were used to analyze the performance of the top 0.1%, 0.3%, 0.5%, 0.7%, 1%, 2%, and 3% of FC metrics. Results showed that 0.5% percentile features performed better, with average 5-fold accuracy of 94%. The study identified significant contributions from dorsal attention (14.75%), cingulo-opercular task control (14.39%), and visual networks (12.59%). This study could be used as an essential brain FC method to diagnose ASD.