Efficient Frequency-Aware k-Core Query on Temporal Graphs

In temporal graphs, time and topology are considered to be intertwined. As an evidence, it is observed that the vertices in more cohesive subgraphs have more frequent and more numerous interactions between each other in the history. Motivated by that, we study a novel frequency-aware k-core query problem. Different from previous studies that focus on finding k-cores in the projected subgraphs of given time intervals, we look for the subgraphs of k-core in which neighbor vertices have at least a certain number of high-frequency interactions. To address the problem, we propose 1) a minimum slope algorithm for computing the frequency in linear time, 2) a space-efficient index that stores the distinct “core frequency” of vertices for addressing arbitrary queries, 3) a propagation algorithm that collects core frequencies by message passing for index construction, and 4) efficient algorithms for retrieving a specific or all skyline results from the index respectively. The experimental results show that, our algorithms achieve several orders of magnitude improvement on efficiency compared to corresponding baselines, and meanwhile, the size of index is even smaller than that of graph unless the graph has very few timestamps on each edge. More importantly, by both statistics and case study, it is verified that the frequency-aware k-core query indeed find more cohesive subgraphs in the static k-core.