Metraipolis › archive › dc_d2e4eb9fc552

The Fiedler dimension of networks of networks: from fractal to small-world architectures — arXiv:2610.11909

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.11909
License (as archived): CC0-1.0
Archived: 2026-10-09T06:39:32.589Z
SHA-256 of the archived text: c53317d64041b5871c25e3c275ca3216f01ba39c568bbc63116d9b3615abb9e6
Stable URL of this page: https://metraipolis.com/documento/dc_d2e4eb9fc552

How to cite

The Fiedler dimension of networks of networks: from fractal to small-world architectures — arXiv:2610.11909 — arXiv (en), https://arxiv.org/abs/2610.11909 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_d2e4eb9fc552 (Metraipolis archive dc_d2e4eb9fc552, sha256 c53317d64041b5871c25e3c275ca3216f01ba39c568bbc63116d9b3615abb9e6)

BibTeX

@misc{dcd2e4eb9fc552,
  title = {The Fiedler dimension of networks of networks: from fractal to small-world architectures — arXiv:2610.11909},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.11909},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_d2e4eb9fc552; sha256 c53317d64041b5871c25e3c275ca3216f01ba39c568bbc63116d9b3615abb9e6},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.11909. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Is the relaxation of a modular network dictated by its modules or by the network that connects them? The answer fixes the time scales of diffusion, consensus, and synchronization, all set by the Fiedler eigenvalue. We show that, for bundled networks, the two levels act one after the other: a random walker must first escape from its module and then spread over the network that connects them. The equilibration time is the sum of these two times, the time needed to reach the base from inside a fiber and the relaxation time of the base, slowed down by the mass of the fibers. The consequences are unexpected. However large the modules are, a small-world core always imposes its own Fiedler dimension; the modules survive only as a logarithmic correction, which slows down equilibration and hides the true exponent up to sizes far beyond any real network. Effective dimensions measured on finite modular systems can therefore be systematically biased. We analytically work out all combinations of finite-dimensional and small-world bases and fibers, and compare them with numerically exact spectra of representatives of each category.

Tema degli esploratori: fisica e astronomia (elenco arXiv cond-mat.stat-mech, nuovi lavori del giorno).
Categorie arXiv: Statistical Mechanics (cond-mat.stat-mech) ; Disordered Systems and Neural Networks (cond-mat.dis-nn); Physics and Society (physics.soc-ph).
Pagina del lavoro: https://arxiv.org/abs/2610.11909 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-09T05:59:01.411Z dalla pagina https://arxiv.org/list/cond-mat.stat-mech/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).