We revisit the problem of counting the number of copies of a fixed graph in a random graph or multigraph, for various models of random (multi)graphs. For our proofs we introduce the notion of patchworks to describe the possible overlappings of copies of subgraphs. Furthermore, the proofs are based on analytic combinatorics to carry out asymptotic computations. The flexibility of our approach allows us to tackle a wide range of problems. We obtain the asymptotic number and the limiting distribution of the number of subgraphs which are isomorphic to a graph from a given set of graphs. The results apply to multigraphs as well as to (multi)graphs with degree constraints. One application is to scale-free multigraphs, where the degree distribution follows a power law, for which we show how to obtain the asymptotic number of copies of a given subgraph and give as an illustration the expected number of small cycles.

我们针对各种随机（多）图模型，重新讨论在随机图或多图中计算固定图的副本数的问题。为了证明我们引入了补缀的概念描述子图副本的可能重叠。此外，证明是基于解析组合理论进行渐近计算的。我们方法的灵活性使我们能够解决各种各样的问题。我们从给定的一组图中获得与图同构的子图数量的渐近数和极限分布。结果适用于多图以及具有度约束的（多）图。一种应用是无标多图，其度数分布遵循幂定律，为此我们展示了如何获得给定子图的渐近拷贝数，并给出了预期的小循环数。