Abstract
We explore the fundamental principles underlying the architecture of the human brain’s structural connectome through the lens of spectral analysis. Building on the idea that the brain balances efficient information processing with minimizing wiring costs, we aimed to understand how the connectome metric properties relate to the presence of an inherent scale. We demonstrate that a simple generative model, combining nonlinear preferential attachment with an exponential penalty for spatial distance, can effectively reproduce several key features of the human connectome. These include spectral density, eigenmode localization, local clustering and topological properties. Additionally, we examine the finer spectral characteristics of human structural connectomes by evaluating the inverse participation ratios across various parts of the spectrum. Our analysis shows that the level statistics in the soft cluster region of the Laplacian spectrum deviate from a Poisson distribution due to interactions between clusters. Furthermore, we identify localized modes with large IPR values in the continuum spectrum. Multiple fractal eigenmodes are found across the spectrum, and we evaluate their fractal dimensions. We also find a power-law behavior in the return probability, a hallmark of critical behavior. We conclude by discussing the conjecture that the brain operates in an extended critical phase that supports multifractality.
Author Summary
In this work, we explore the fundamental principles underlying the architecture of the human structural connectome. We use a simple generative model that combines nonlinear preferential attachment with biologically plausible geometric constraints. This model successfully reproduces a remarkable number of brain network properties, linking the overall architecture of the brain to its underlying evolutionary principles. Additionally, we investigate the localization properties of connectome eigenmodes and identify multiple indications of their fractality. Drawing on recent advances in Anderson localization in complex systems, we conjecture that the structural connectome operates in an extended critical phase that supports multifractality.
Author notes
Handling Editor: Richard Betzel