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Largest connected component in duplication-divergence growing graphs with symmetric coupled divergence

Dario Borrelli*

  • *Contact author: dario.borrelli@unina.it
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Phys. Rev. E 114, L052301 – Published 9 November, 2026

DOI: https://doi.org/10.1103/3zrx-56mx

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 δc. The δc found is close to the locus of zero in Euler characteristic of finite-size graphs known to reflect the proximity of the largest connected component transition. A close correspondence with the vanishing of a scaling relation exponent for moments of the vertex degree distribution is shown, with such a scaling relation that generalizes a known form for duplication-divergence model graphs. The role of noninteracting vertices in shaping this transition with their presence or absence in duplication is also considered through a particular relation which would result in the two cases being comparable. The findings have relevancy for bond percolation in these growing graph models.

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Outline

Information

Phys. Rev. E 114, L052301– Published 9 November, 2026
  • Received 12 January 2026
  • Revised 6 August 2026
  • Accepted 16 September 2026
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