Simple linear algorithms for mining graph cores

Batagelj and Zaversnik proposed a linear algorithm for the wellknown k-core decomposition problem. However, when k-cores are desired for a given k, we find that a simple linear algorithm requiring no sorting works for mining k-cores. In addition, this algorithm can be extended to mine (k1, k2, . . . , kp)-cores from p-partite graphs in linear time, and this mining approach can be efficiently implemented in a distributed computing environment with a lower message complexity bound in comparison with the best known method of distributed k-core decomposition.