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The paper deals with a random connection model, a random graph whose verticesare given by a homogeneous Poisson point process on $\mathbb{R}^d$, and edgesare independently drawn with probability depending on the locations of the twoend points. We establish central limit theorems (CLT) for general functionalson this graph under minimal assumptions that are a combination of the weakstabilization for the-one cost and a $(2+\delta)$-moment condition. As aconsequence, CLTs for isomorphic subgraph counts, isomorphic component counts,the number of connected components are then derived. In addition, CLTs forBetti numbers and the size of biggest component are also proved for the firsttime.

Random connection models in the thermodynamic regime: central limit theorems for add-one cost stabilizing functionals