gCore: Exploring Cross-Layer Cohesiveness in Multi-Layer Graphs

As multi-layer graphs can give a more accurate and reliable picture of the complex relationships between entities, cohesive subgraph mining, a fundamental task in graph analysis, has been studied on multi-layer graphs in the literature. However, existing cohesive subgraph models are designated for special multi-layer graphs such as multiplex networks and heterogeneous information networks. In this paper, we propose generalized core (gCore), a new notion of cohesive subgraph on general multi-layer graphs without any predefined constraints on the interconnections between vertices. The gCore model considers both the intra-layer and cross-layer cohesiveness of vertices. Three related problems are studied in this paper including gCore search (GCS), gCore decomposition (GCD), and gCore indexing (GCI). A polynomial-time algorithm based on the peeling paradigm is proposed to solve the GCS problem. By considering the containment among gCores, a "tree of trees" data structure called KP-tree is designed for efficiently solving the GCD problem and serving as a compact storage and index of all gCores. Several advanced lossless compaction techniques including node/subtree elimination, subtree transplant, and subtree merge are proposed to help reduce the storage overhead of the KP-tree and speed up the process of solving GCD and GCI. Besides, a KP-tree-based GCS algorithm is designed, which can retrieve any gCore in linear time in the size of the gCore and the height of the KP-tree. The experiments on 10 real-world graphs verify the effectiveness of the gCore model and the efficiency of the proposed algorithms.