Graphs are widely used to represent the abundant information in social networks for discovering promising communities, reinforcing network stability, and finding critical users, to name a few. Cohesive subgraph mining, as one of the most fundamental problems in graphs, gains increasing popularity in social network study for its effectiveness. In this thesis, some basic social components are considered in cohesive subgraphs to better accommodate various real-life applications.
Firstly, we investigate the problem of (k,r)-core which intends to find cohesive subgraphs on social networks considering both user engagement and similarity. Efficient algorithms are proposed to enumerate all maximal (k,r)-cores and find the maximum (k,r)-core, where both problems are shown to be NP-hard. Effective pruning techniques and search orders substantially reduce the search space of two algorithms. A novel upper bound enhances performance of the maximum (k,r)-core computation. Comprehensive experiments on real-life data demonstrate that the algorithms efficiently find interesting communities.
Secondly, we study the problem of the anchored k-core, which was introduced by Bhawalkar and Kleinberg et al. in the context of user engagement in social networks. The problem has been shown to be NP-hard and inapproximable. We propose an efficient algorithm, namely OLAK, as the first to solve the problem on general graphs. An onion layer structure is designed together with efficient candidates exploration, early termination and pruning techniques to significantly simplify computation and greatly reduce the search space.
Besides considering user engagement, we further explore the unraveling phenomenon with tie strength, which leads us to the model of k-truss. We then investigate the anchored k-truss problem which is also NP-hard and propose an edge onion layer structure based algorithm, namely AKT. Efficient candidate exploration and pruning techniques are designed based on the edge onion layers. Comprehensive experiments on real-life graphs for the above two problems demonstrate the effectiveness and efficiency of our proposed methods.
Finally, we study the leave of critical users, which may greatly break network engagement. Accordingly, we propose the collapsed k-core problem to find the vertices whose leave can lead to the smallest k-core. We prove the problem is NP-hard. Then, an efficient algorithm is proposed, which significantly reduces the number of candidate vertices to speed up computation. Comprehensive experiments on real-life social networks demonstrate effectiveness of the model and efficiency of the proposed techniques.