This study proposes a new approach that investigates differences in topological characteristics of visual networks, which are constructed using fMRI BOLD time-series corresponding to visual datasets of COCO, ImageNet, and SUN. A publicly available BOLD5000 dataset is utilized that contains fMRI scans while viewing 5254 images of diverse complexities. The objective of this study is to examine how network topology differs in response to distinct visual stimuli from these visual datasets. To achieve this, 0- and 1-dimensional persistence diagrams are computed for each visual network representing COCO, ImageNet, and SUN. For extracting suitable features from topological persistence diagrams, K-means clustering is executed. The extracted K-means cluster features are fed to a novel deep-hybrid model that yields accuracy in the range of 90%-95% in classifying these visual networks. To understand vision, this type of visual network categorization across visual datasets is important as it captures differences in BOLD signals while perceiving images with different contexts and complexities. Furthermore, distinctive topological patterns of visual network associated with each dataset, as revealed from this study, could potentially lead to the development of future neuroimaging biomarkers for diagnosing visual processing disorders like visual agnosia or prosopagnosia, and tracking changes in visual cognition over time.