Community identification in social networks is of great interest and with dynamic changes to its graph representation and content, the incremental maintenance of community poses significant challenges in computation. Moreover, the intensity of community engagement can be distinguished at multiple levels, resulting in a multi-resolution community representation that has to be maintained over time. In this paper, we first formalize this problem using the k-core metric projected at multiple k values, so that multiple community resolutions are represented with multiple k-core graphs. We then present distributed algorithms to construct and maintain a multi-k-core graph, implemented on the scalable big-data platform Apache HBase. Our experimental evaluation results demonstrate orders of magnitude speedup by maintaining multi-k-core incrementally over complete reconstruction. Our algorithms thus enable practitioners to create and maintain communities at multiple resolutions on different topics in rich social network content simultaneously. © 2013 IEEE.