Lienau, MatthiasMatthiasLienau2025-11-132025-11-132025-11-03Journal of Applied Probability (in Press): (2025)https://hdl.handle.net/11420/58726The generalised random graph contains n vertices with positive i.i.d. weights. The probability of adding an edge between two vertices is increasing in their weights. We require the weight distribution to have finite second moments, and study the point process Cn on {3,4,…}, which counts how many cycles of the respective length are present in the graph. We establish convergence of Cn to a Poisson point process. Under the stronger assumption of the weights having finite fourth moments we provide the following results. When Cn is evaluated on a bounded set A, we provide a rate of convergence. If the graph is additionally subcritical, we extend this to unbounded sets A at the cost of a slower rate of convergence. From this we deduce the limiting distribution of the length of the shortest and longest cycles when the graph is subcritical, including rates of convergence. All mentioned results also apply to the Chung–Lu model and the Norros–Reittu model.en0021-90022025Cambridge University Press (CUP)Technology::600: TechnologyJournal Article10.1017/jpr.2025.10035Journal Article