Maximal D-truss Search in Dynamic Directed Graphs

Community search (CS) aims at personalized subgraph discovery which is the key to understanding the organisation of many real-world networks. CS in undirected networks has attracted significant attention from researchers, including many solutions for various cohesive subgraph structures and for different levels of dynamism with edge insertions and deletions, while they are much less considered for directed graphs. In this paper, we propose incremental solutions of CS based on the D-truss in dynamic directed graphs, where the D-truss is a cohesive subgraph structure defined based on two types of triangles in directed graphs. We first analyze the theoretical boundedness of D-truss given edge insertions and deletions, then we present basic single-update algorithms. To improve the efficiency, we propose an order-based D-Index, associated batch-update algorithms and a fully-dynamic query algorithm. Our extensive experiments on real-world graphs show that our proposed solution achieves a significant speedup compared to the SOTA solution, the scalability over updates is also verified.