{
  "annotation_id": "b0df4914-d55e-4bb6-ab50-7487e22451e1",
  "date_created": "2026-02-17T05:53:08.659000Z",
  "date_modified": "2026-02-17T05:53:08.659000Z",
  "file_hash": "6f76ca093e4d3ba10a52eed2d01cff5ef83fbc4ecb944ae07ca74b4bb23be44d",
  "private": false,
  "record": {
    "abstract": "The largest connected component in duplication-divergence growing graphs with symmetric coupled divergence is studied. Finite-size scaling reveals a phase transition occurring at a divergence rate $\\delta_c$. The $\\delta_c$ found stands near the locus of zero in Euler characteristic for finite-size graphs, known to be indicative of the largest connected component transition. The role of non-interacting vertices in shaping this transition, with their presence ($d=0$) and absence ($d=1$) in duplication is also discussed, suggesting a particular transformation of the time variable considered yielding a singularity locus in the natural logarithm of the absolute value of Euler characteristic in finite-size graphs close to that obtained with $d=1$ but from the model with $d=0$. The findings may suggest implications for bond percolation in these growing graph models.",
    "arxiv_id": "2601.07024",
    "authors": [
      "Dario Borrelli"
    ],
    "categories": [
      "cond-mat.stat-mech",
      "nlin.AO",
      "physics.soc-ph",
      "q-bio.MN"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Largest connected component in duplication-divergence growing graphs with symmetric coupled divergence",
    "url": "https://arxiv.org/abs/2601.07024",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4992d533-4841-4cef-9b26-423123acb0e5",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}