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

arXiv:2601.07024v3 Announce Type: replace-cross
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, 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.