Abstract
The structural network of the human brain has a rich topology which many have sought to characterise using standard network science measures and concepts. However, this characterisation remains incomplete and the non-obvious features of this topology have confounded attempts to model it constructively. This calls for new perspectives. Hierarchical complexity is an emerging paradigm of complex network topology based on the observation that complex systems are composed of hierarchies within which the roles of hierarchically equivalent nodes display highly variable connectivity patterns. Here we test the hierarchical complexity of the human structural connectomes of a group of seventy-nine healthy adults. Binary connectomes are found to be more hierarchically complex than three null models — random graphs, random geometric graphs, and edge-randomised connectomes. This presents important new insights into the structure of the human brain, indicating a rich variety of connectivity patterns within hierarchically equivalent nodes. That random models fail to show such behaviour suggests that the generative mechanisms of brain structure may even insist on such dissimilarity. This also provides the strongest evidence to date in support of the hierarchical complexity paradigm of complex brain networks — both ordered and random systems are inherently more predictable. Dividing the connectomes into four tiers based on degree magnitudes indicates that the most complex nodes are neither those with the highest nor lowest degrees but are instead found in the third and second tiers. Spatial mapping of the brain regions in each hierarchical tier reveals consistency with the current anatomical, functional and neuropsychological knowledge of the human brain. The most complex tier (tier 3) involves regions believed to bridge high-order cognitive (tier 1) and low-order sensorimotor processing (tier 2), revealing a strikingly large diversity of connectivity patterns elicited in the integration of these processes.