Largest connected component in duplication-divergence growing graphs with symmetric coupled divergence
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908788203716608 |
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| author | Borrelli, Dario |
| author_facet | Borrelli, Dario |
| contents | 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 $δ_c$. The $δ_c$ 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, which yields a singularity locus in the natural logarithm of the absolute value of Euler characteristic in finite-size graphs near 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_07024 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Largest connected component in duplication-divergence growing graphs with symmetric coupled divergence Borrelli, Dario Statistical Mechanics Adaptation and Self-Organizing Systems Physics and Society Molecular Networks 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 $δ_c$. The $δ_c$ 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, which yields a singularity locus in the natural logarithm of the absolute value of Euler characteristic in finite-size graphs near 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. |
| title | Largest connected component in duplication-divergence growing graphs with symmetric coupled divergence |
| topic | Statistical Mechanics Adaptation and Self-Organizing Systems Physics and Society Molecular Networks |
| url | https://arxiv.org/abs/2601.07024 |