Property graphs can be used to represent heterogeneous networks with labeled (attributed) vertices and edges. Given a property graph, simulating another graph with same or greater size with the same statistical properties with respect to the labels and connectivity is critical for privacy preservation and benchmarking purposes. In this work we tackle the problem of capturing the statistical dependence of the edge connectivity on the vertex labels and using the same distribution to regenerate property graphs of the same or expanded size in a scalable manner. However, accurate simulation becomes a challenge when the attributes do not completely explain the network structure. We propose the Property Graph Model (PGM) approach that uses a label augmentation strategy to mitigate the problem and preserve the vertex label and the edge connectivity distributions as well as their correlation, while also replicating the degree distribution. Our proposed algorithm is scalable with a linear complexity in the number of edges in the target graph. We illustrate the efficacy of the PGM approach in regenerating and expanding the datasets by leveraging two distinct illustrations. Our open-source implementation is available on GitHub.