A moment-generating formula for Erdős-Rényi component sizes

[摘要] We derive a simple formula characterizing the distribution of the size of the connected component of a fixed vertex in the Erdős-Rényi random graph which allows us to give elementary proofs of some results of [9] and [12] about the susceptibility in the subcritical graph and the CLT [17] for the size of the giant component in the supercritical graph.

[学科分类] 统计和概率

[关键词] Erdős-Rényi graph;generating function;susceptibility;giant component;central limit theorem