Multivariate Poisson approximation of joint subgraph counts in random graphs via size-biased couplings

Using Chen-Stein method in combination with size-biased couplings, we obtain the multivariate Poisson approximation in terms of the Wasserstein distance. As applications, we study the multivariate Poisson approximation of the distribution of joint subgraph counts in an Erdős-Rényi random graph and the multivariate hypergeometric distribution giving explicit convergence rates.