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Assortativity and the Distribution of Spectral Gaps in Directed Networks — arXiv:2610.41295

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.41295
License (as archived): CC0-1.0
Archived: 2026-11-02T04:48:26.985Z
SHA-256 of the archived text: 579bb852f0a3c1816ba28651e236243c9dfbbed2950f9b0c5236f54079ad6de2
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Assortativity and the Distribution of Spectral Gaps in Directed Networks — arXiv:2610.41295 — arXiv (en), https://arxiv.org/abs/2610.41295 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_3dfdaeb648d7 (Metraipolis archive dc_3dfdaeb648d7, sha256 579bb852f0a3c1816ba28651e236243c9dfbbed2950f9b0c5236f54079ad6de2)

BibTeX

@misc{dc3dfdaeb648d7,
  title = {Assortativity and the Distribution of Spectral Gaps in Directed Networks — arXiv:2610.41295},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.41295},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_3dfdaeb648d7; sha256 579bb852f0a3c1816ba28651e236243c9dfbbed2950f9b0c5236f54079ad6de2},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.41295. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

This paper studies how the distribution of spectral gaps of a weighted directed network varies with its assortativity. We prove that the sum of the distances of each of the eigenvalues from the Perron root along the real axis, which we call the `spectral depth', decreases as the network is rewired to be less assortative. The result is conditional on the network's Perron vectors ordering the rewired vertices in the same way as their strengths do. We also develop a method to determine whether a particular spectral gap contracts or expands under a rewiring that changes the network's assortativity. It turns out that the direction of any one gap depends on far more than the network's assortativity. In computational experiments on heavy-tailed networks, disassortative rewiring lowers the spectral depth by about two fifths, contracts most strongly the gaps in the middle of the spectrum, and collapses a growing part of the spectrum to zero. The experiments also show that a sequence of disassortative rewirings tends to narrow the first spectral gap, while a sequence of assortative rewirings widens it.

Tema degli esploratori: governance digitale e beni comuni (elenco arXiv cs.SI, nuovi lavori del giorno).
Categorie arXiv: Social and Information Networks (cs.SI).
Pagina del lavoro: https://arxiv.org/abs/2610.41295 — 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 2026-11-02T04:44:27.721Z dalla pagina https://arxiv.org/list/cs.SI/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).