Though widely hypothesized, limited evidence exists that human brain functions organize in global gradients of abstraction starting from sensory cortical inputs. Hierarchical representation is accepted in computational networks, and tentatively in visual neuroscience, yet no direct holistic demonstrations exist in vivo. Our methods developed network models enriched with tiered directionality, by including input locations, a critical feature for localizing representation in networks generally. Grouped primary sensory cortices defined network inputs, displaying global connectivity to fused inputs. Depth-oriented networks guided analyses of fMRI databases (~17,000 experiments;~1/4 of fMRI literature). Formally, we tested whether network depth predicted localization of abstract versus concrete behaviors over the whole set of studied brain regions. For our results, new cortical graph metrics, termed network-depth, ranked all databased cognitive function activations by network-depth. Thus, we objectively sorted stratified landscapes of cognition, starting from grouped sensory inputs in parallel, progressing deeper into cortex. This exposed escalating amalgamation of function or abstraction with increasing network-depth, globally. Nearly 500 new participants confirmed our results. In conclusion, data-driven analyses defined a hierarchically ordered connectome, revealing a related continuum of cognitive function. Progressive functional abstraction over network depth may be a fundamental feature of brains, and is observed in artificial networks.