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.