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To support the ever-increasing data traffic demands, the Internet has been experiencing a rapid growth in recent decades. Effective and efficient monitoring is highly needed in order to properly manage such complex infrastructure. It is of theoretical and practical significance to derive network device importance (i.e., node rank) for resource utilization optimization, user experience improvement, and security enhancement. Recent development in the Internet infrastructure has introduced prosperous in-network computation resources across the network. To exploit such distributed resources, in this article, we propose a core-graphbased framework, called FRank, for fast node ranking algorithms, which accelerates convergence and reduces communication cost by converting most inter-partition state change propagations into intra-partition ones. We have implemented FRank in a cluster to validate its correctness and efficiency. The experiment results demonstrate that at the least FRank reduces the execution time of existing cutting-edge methods by 30.2 percent with 43.5 percent less communication cost. [ABSTRACT FROM AUTHOR]