Abstract
The idea that complex systems have a hierarchical modular organization originated in the early 1960s and has recently attracted fresh support from quantitative studies of large scale, real-life networks. Here we investigate the hierarchical modular (or “modules-within-modules”) decomposition of human brain functional networks, measured using functional magnetic resonance imaging in 18 healthy volunteers under no-task or resting conditions. We used a customized template to extract networks with more than 1800 regional nodes, and we applied a fast algorithm to identify nested modular structure at several hierarchical levels. We used mutual information, 0 < I < 1, to estimate the similarity of community structure of networks in different subjects, and to identify the individual network that is most representative of the group. Results show that human brain functional networks have a hierarchical modular organization with a fair degree of similarity between subjects, I = 0.63. The largest five modules at the highest level of the hierarchy were medial occipital, lateral occipital, central, parieto-frontal and fronto-temporal systems; occipital modules demonstrated less sub-modular organization than modules comprising regions of multimodal association cortex. Connector nodes and hubs, with a key role in inter-modular connectivity, were also concentrated in association cortical areas. We conclude that methods are available for hierarchical modular decomposition of large numbers of high resolution brain functional networks using computationally expedient algorithms. This could enable future investigations of Simon's original hypothesis that hierarchy or near-decomposability of physical symbol systems is a critical design feature for their fast adaptivity to changing environmental conditions.
Highlights
Almost 50 years ago, Herbert Simon wrote an essay entitled “The architecture of complexity” (Simon, 1962)
There was a significant increase in brain network modularity compared to random network modularity (Kolmogorov–Smirnov test, D = 1, P ∼ 2−10)
In order to show the robustness of our results, we propose to look at the resilience of the hierarchical modular organization under the tuning of the value of m
Summary
Almost 50 years ago, Herbert Simon wrote an essay entitled “The architecture of complexity” (Simon, 1962). In this prescient analysis, he argued that most complex systems, such as social, biological and physical symbolic systems, are organized in a hierarchical manner. He argued that most complex systems, such as social, biological and physical symbolic systems, are organized in a hierarchical manner He introduced the notion of “nearly-decomposable systems”, i.e. systems where elements have most of their interactions (of any kind) with a subset of elements in some sense close to them, and much less interaction with elements outside this subset. Decomposability, or modularity, accelerates the emergence of complex systems from simple systems by providing stable intermediate forms (component modules) that allow the system to adapt one module at a time without risking loss of function in other, already-adapted modules
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