Efficient temporal core maintenance of massive graphs

Abstract

k−core is a cohesive subgraph such that every vertex has at least k neighbors within the subgraph, which provides a good measure to evaluate the importance of vertices as well as their connections. Unfortunately, k−core cannot adequately reveal the structure of a temporal graph, in which two vertices may connect multiple edges containing time information. As a result, (k,h)−core is derived from k−core, which is also called temporal core, to provide a well-formulated definition, where h represents the number of temporal edges between two vertices. However, it is costly to repeatedly decompose a temporal graph changing over time.To address this challenge, we study the method of (k,h)−core maintenance, which can find current (k,h)−cores with less computational efforts. To estimate the influence scope of inserted (removed) edges, we propose quasi-temporal core, denoted by quasi−(k,h)−core, which relaxes the constraint of (k,h)−core but still has similar properties to (k,h)−core. With the aid of quasi−(k,h)−core, our insertion algorithm finds the minimum incremental graph for each influenced (k,h)−core, and the removal algorithm adjusts each influenced (k,h)−core in the minimal range. Experimental results verify effectiveness and scalability of our proposed algorithms.