The co-occurrence of Autism Spectrum Disorder and Epilepsy, i.e., ASD + E is very common, however, the underlying mechanism associating both cohorts has not been unraveled quantitatively yet. Using resting-state EEG, the present work investigates whether brain functional topology can explain and differentiate ASD + E from ASD and E. A weighted visibility graph (VG) algorithm is employed to map brain EEG signals of 120 age-matched ASD (30), E (30), ASD + E (30) and Typically Developing (TD; 30) individuals into a complex network. Afterward, the complex graph metrics were evaluated to measure brain connectivity at local and global level. The proposed methodology is compared with state-of-art-methods in disorder detection. The statistical and probabilistic investigations have shown that ASD + E affects the brain network topology majorly in frontal, temporal, and parietal regions, but it shows a functional overlap with ASD (49%) and epilepsy (55%). Furthermore, the evaluation of the metrics using Support Vector Machine (SVM) classifier reflected that a combination of metrics (average weighted degree, local efficiency, characteristic path length, and eigenvector centrality) can distinguish the groups with an accuracy of 98.2%. The paper also demonstrated that variation in brain topology with maturation (from child (5–11 years) to adolescent (11–18 years)) is the reason for heterogeneity and unexplained behavioral abnormalities in affected individuals. In contrast to existing theoretical studies, the present study has quantitatively ruled out ASD + E condition by tracing variations in brain regions and network topology. In future, the studies can target the identified regions to detect evident clinical markers responsible for ASD, E and ASD + E as well.