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The core number of a vertex is a basic index depicting cohesiveness of agraph, and has been widely used in large-scale graph analytics. In this paper,we study the update of core numbers of vertices in dynamic graphs with edgeinsertions/deletions, which is known as the core maintenance problem. Differentfrom previous approaches that just focus on the case of single-edgeinsertion/deletion and sequentially handle the edges when multiple edges areinserted/deleted, we investigate the parallelism in the core maintenanceprocedure. Specifically, we show that if the inserted/deleted edges constitutea matching, the core number update with respect to each inserted/deleted edgecan be handled in parallel. Based on this key observation, we propose parallelalgorithms for core maintenance in both cases of edge insertions and deletions.We conduct extensive experiments to evaluate the efficiency, stability,parallelism and scalability of our algorithms on different types of real-worldand synthetic graphs. Comparing with sequential approaches, our algorithms canimprove the core maintenance efficiency significantly.

Core Maintenance in Dynamic Graphs: A Parallel Approach based on Matching