Synthetic graph generators facilitate research in graph algorithms and processing systems by providing access to data, for instance, graphs resembling social networks, while circumventing privacy and security concerns. Nevertheless, their practical value lies in their ability to capture important metrics of real graphs, such as degree distribution and clustering properties. Graph generators must also be able to produce such graphs at the scale of real-world industry graphs, that is, hundreds of billions or trillions of edges. In this paper, we propose Darwini, a graph generator that captures a number of core characteristics of real graphs. Importantly, given a source graph, it can reproduce the degree distribution and, unlike existing approaches, the local clustering coefficient and joint-degree distributions. Furthermore, Darwini maintains metrics such node PageRank, eigenvalues and the K-core decomposition of a source graph. Comparing Darwini with state-of-the-art generative models, we show that it can reproduce these characteristics more accurately. Finally, we provide an open source implementation of our approach on the vertex-centric Apache Giraph model that allows us to create synthetic graphs with one trillion edges.