FACH: Fast algorithm for detecting cohesive hierarchies of communities in large networks

Vertices in a real-world social network can be grouped into densely connected communities that are sparsely connected to other groups. Moreover, these communities can be partitioned into successively more cohesive communities. Despite an ever-growing pile of research on hierarchical community detection, existing methods suffer from either inefficiency or inappropriate modeling. Yet, some cut-based approaches have shown to be effective in finding communities without hierarchies. In this paper, we study the hierarchical community detection problem in large networks and show that it is NP-hard. We then propose an efficient algorithm based on edge-cuts to identify the hierarchy of communities. Since communities at lower levels of the hierarchy are denser than the higher levels, we leverage a fast network sparsification technique to enhance the running time of the algorithm. We further propose a randomized approximation algorithm for information centrality of networks. We finally evaluate the performance of the proposed algorithms by conducting extensive experiments using real datasets. Our experimental results show that the proposed algorithms are promising and outperform the state-of-the-art algorithms by several orders of magnitude.This work is supported by the grant of Australian Research Council Discovery Project No. DP120102627

Efficient Algorithms for the Identification of Top-k Structural Hole Spanners in Large Social Networks

Recent studies show that individuals in a social network can be divided into different groups of densely connected communities, and these individuals who bridge different communities, referred to as structural hole spanners, have great potential to acquire resources/information from communities and thus benefit from the access. Structural hole spanners are crucial in many real applications such as community detections, diffusion controls, viral marketing, etc. In spite of their importance, little attention has been paid to them. Particularly, how to accurately characterize the structural hole spanners and how to devise efficient yet scalable algorithms to find them in a large social network are fundamental issues. In this paper, we study the top-k structural hole spanner problem. We first provide a novel model to measure the quality of structural hole spanners through exploiting the structural hole spanner properties. Due to its NP-hardness, we then devise two efficient yet scalable algorithms, by developing innovative filtering techniques that can filter out unlikely solutions as quickly as possible, while the proposed techniques are built up on fast estimations of the upper and lower bounds on the cost of an optimal solution and make use of articulation points in real social networks. We finally conduct extensive experiments to validate the effectiveness of the proposed model, and to evaluate the performance of the proposed algorithms using real world datasets. The experimental results demonstrate that the proposed model can capture the characteristics of structural hole spanners accurately, and the structural hole spanners found by the proposed algorithms are much better than those by existing algorithms in all considered social networks, while the running times of the proposed algorithms are very fastWenzheng Xu’s work was supported by National Natural Science Foundation of China (Grant No. 61602330) and 2016 Research Talent Foundation of Sichuan University in China (Grant No. 2082204194050). Also, this work is funded by the grant of Australian Research Council Discovery Project No. DP120102627