Graph partitioning is an enabling technology for parallel processing as it allows for the effective decomposition of unstructured computations whose data dependencies correspond to a large sparse and irregular graph. Even though the problem of computing high-quality partitionings of graphs arising in scientific computations is to a large extent well-understood, this is far from being true for emerging HPC applications whose underlying computation involves graphs whose degree distribution follows a power-law curve. This paper presents new multilevel graph partitioning algorithms that are specifically designed for partitioning such graphs. It presents new clustering-based coarsening schemes that identify and collapse together groups of vertices that are highly connected. An experimental evaluation of these schemes on 10 different graphs show that the proposed algorithms consistently and significantly outperform existing state-of-the-art approaches.