Graph clustering or community detection constitutes an important task for investigating the internal structure of graphs, with a plethora of applications in several domains. Traditional techniques for graph clustering, such as spectral methods, typically suffer from high time and space complexity. In this article, we present CoreCluster, an efficient graph clustering framework based on the concept of graph degeneracy, that can be used along with any known graph clustering algorithm. Our approach capitalizes on processing the graph in an hierarchical manner provided by its core expansion sequence, an ordered partition of the graph into different levels according to the k-core decomposition. Such a partition provides an efficient way to process the graph in an incremental manner that preserves its clustering structure, while making the execution of the chosen clustering algorithm much faster due to the smaller size of the graph's partitions onto which the algorithm operates. An experimental analysis on a multitude of real and synthetic data demonstrates that our approach can be applied to any clustering algorithm accelerating the clustering process, while the quality of the clustering structure is preserved or even improved.