The spectral dimension is a generalization of the Euclidean dimension and quantifies the propensity of a network to transmit and diffuse information. We show that in hierarchical-modular network models of the brain, dynamics are anomalously slow and the spectral dimension is not defined. Inspired by Anderson localization in quantum systems, we relate the localization of neural activity—essential to embed brain functionality—to the network spectrum and to the existence of an anomalous “Lifshitz dimension.” In a broader context, our results help shed light on the relationship between structure and function in biological information-processing complex networks.

• Received 28 August 2020
• Accepted 23 October 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.043291

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society