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Asymptotic Properties of Random Unlabelled Block-Weighted Graphs
2021
Electronic Journal of Combinatorics
We study the asymptotic shape of random unlabelled graphs subject to certain subcriticality conditions. The graphs are sampled with probability proportional to a product of Boltzmann weights assigned to their $2$-connected components. As their number of vertices tends to infinity, we show that they admit the Brownian tree as Gromov–Hausdorff–Prokhorov scaling limit, and converge in a strengthened Benjamini–Schramm sense toward an infinite random graph. We also consider models of random graphs
doi:10.37236/9923
fatcat:4ovuurqmrfcgxlon3kh5ifbbbu