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Spectral coarse graining and rescaling for preserving structural and dynamical properties in graphs

M. Schmidt, F. Caccioli, and T. Aste

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Phys. Rev. E 112, 034303 – Published 2 September, 2025

DOI: https://doi.org/10.1103/k4bx-w273

Abstract

We introduce a graph renormalization procedure based on the coarse-grained Laplacian, which generates reduced-complexity representations across scales. This method retains both dynamics and large-scale topological structures, while reducing redundant information, facilitating the analysis of large graphs by decreasing the number of vertices. Applied to graphs derived from electroencephalogram recordings of human brain activity, our approach reveals collective behavior emerging from neuronal interactions, such as coordinated neuronal activity. Additionally, it shows dynamic reorganization of brain activity across scales, with more generalized patterns during rest and more specialized and scale-invariant activity in the occipital lobe during attention.

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Information

Phys. Rev. E 112, 034303– Published 2 September, 2025
  • Received 20 December 2024
  • Accepted 11 August 2025
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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.

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