“…The k-core can be computed by using core decomposition algorithm, while the core decomposition is to efficiently compute for each vertex its core number [4]. Besides, with the dynamic change of the graph, incrementally computing the new core number of each affected vertices is known as core maintenance, which has been studied in [1], [3], [15], [23], [28], [35], [36]. Anchored k-core Problem: User engagement in social networks has attracted much attention while quantifying user engagement dynamics in social networks is usually measured by using kcore [5], [7], [11], [20], [24], [31], [32], [34], [37].…”