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

## TL;DR

This paper introduces parallel algorithms for updating core numbers in dynamic graphs, leveraging matching-based edge updates to significantly improve efficiency over sequential methods.

## Contribution

The paper presents novel parallel algorithms for core maintenance in dynamic graphs, exploiting matching properties to handle multiple edge updates simultaneously.

## Key findings

- Parallel algorithms outperform sequential ones in efficiency.
- Algorithms demonstrate high scalability on real-world and synthetic graphs.
- Significant speedup achieved in core number updates.

## Abstract

The core number of a vertex is a basic index depicting cohesiveness of a graph, 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 edge insertions/deletions, which is known as the core maintenance problem. Different from previous approaches that just focus on the case of single-edge insertion/deletion and sequentially handle the edges when multiple edges are inserted/deleted, we investigate the parallelism in the core maintenance procedure. Specifically, we show that if the inserted/deleted edges constitute a matching, the core number update with respect to each inserted/deleted edge can be handled in parallel. Based on this key observation, we propose parallel algorithms 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-world and synthetic graphs. Comparing with sequential approaches, our algorithms can improve the core maintenance efficiency significantly.