Efficient $k$k-Plex Mining in Temporal Graphs

Yanping Wu, Renjie Sun, Xiaoyang Wang, Ying Zhang, Lu Qin, Wenjie Zhang, Xuemin Lin

Abstract: A $k$-plex is a subgraph in which each vertex can miss edges to at most $k$ vertices, including itself. $k$-plex can find many real-world applications such as social network analysis and product recommendation. Previous studies about $k$-plex mainly focus on static graphs. However, in reality, relationships between two entities often occur at some specific timestamps, which can be modeled as temporal graphs. Directly extending the $k$-plex model may fail to find some critical groups in temporal graphs, which exhibit certain frequent occurring patterns. To fill the gap, in this paper, we develop a novel model, named $(k,l)$-plex, which is a vertex set that exists in no less than $l$ timestamps, at each of which the subgraph induced is a $k$-plex. To identify practical results, we propose and investigate two important problems, i.e., large maximal $(k,l)$-plex (MalKLP) enumeration and maximum $(k,l)$-plex (MaxKLP) identification. For the MalKLP enumeration problem, a reasonable baseline method is first proposed by extending the Bron-Kerbosch (BK) framework. To overcome the limitations in baseline and scale for large graphs, optimized strategies are developed, including novel graph reduction approach and search branch pruning techniques. For the MaxKLP identification task, we first design a baseline method by extending the proposed enumeration framework. Additionally, to accelerate the search, a new search framework with efficient branch pruning rules and refined graph reduction method is developed. Finally, comprehensive experiments are conducted on 14 real-world datasets to validate the efficiency and effectiveness of the proposed techniques.

External IDs:dblp:journals/tkde/WuSWZQZL25