DSPC: Efficiently Answering Shortest Path Counting on Dynamic Graphs (2307.05918v1)

Abstract: The widespread use of graph data in various applications and the highly dynamic nature of today's networks have made it imperative to analyze structural trends in dynamic graphs on a continual basis. The shortest path is a fundamental concept in graph analysis and recent research shows that counting the number of shortest paths between two vertices is crucial in applications like potential friend recommendation and betweenness analysis. However, current studies that use hub labeling techniques for real-time shortest path counting are limited by their reliance on a pre-computed index, which cannot tackle frequent updates over dynamic graphs. To address this, we propose a novel approach for maintaining the index in response to changes in the graph structure and develop incremental (IncSPC) and decremental (DecSPC) update algorithms for inserting and deleting vertices/edges, respectively. The main idea of these two algorithms is that we only locate the affected vertices to update the index. Our experiments demonstrate that our dynamic algorithms are up to four orders of magnitude faster processing for incremental updates and up to three orders of magnitude faster processing for hybrid updates than reconstruction.