Abstract: Clustering large-scale networks is a central topic in unsupervised learning with many applications in machine learning and data mining. A classic approach to cluster a network is to identify regions of high edge density, which in the literature is captured by two fundamental problems: the densest subgraph and the $k$-core decomposition problems. We design massively parallel computation (MPC) algorithms for these problems that are considerably faster than prior work. In the case of $k$-core decomposition, our work improves exponentially on the algorithm provided by Esfandiari et al.~(ICML'18). Compared to the prior work on densest subgraph presented by Bahmani et al.~(VLDB'12, '14), our result requires quadratically fewer MPC rounds. We complement our analysis with an experimental scalability analysis of our techniques.