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The $k$-core decomposition in a graph is a fundamental problem for socialnetwork analysis. The problem of $k$-core decomposition is to calculate thecore number for every node in a graph. Previous studies mainly focus on$k$-core decomposition in a static graph. There exists a linear time algorithmfor $k$-core decomposition in a static graph. However, in many real-worldapplications such as online social networks and the Internet, the graphtypically evolves over time. Under such applications, a key issue is tomaintain the core number of nodes given the graph changes over time. A simpleimplementation is to perform the linear time algorithm to recompute the corenumber for every node after the graph is updated. Such simple implementation isexpensive when the graph is very large. In this paper, we propose a newefficient algorithm to maintain the core number for every node in a dynamicgraph. Our main result is that only certain nodes need to update their corenumber given the graph is changed by inserting/deleting an edge. We devise anefficient algorithm to identify and recompute the core number of such nodes.The complexity of our algorithm is independent of the graph size. In addition,to further accelerate the algorithm, we develop two pruning strategies byexploiting the lower and upper bounds of the core number. Finally, we conductextensive experiments over both real-world and synthetic datasets, and theresults demonstrate the efficiency of the proposed algorithm.

Efficient Core Maintenance in Large Dynamic Graphs