Mixed-case community detection problem in social networks: Algorithms and analysis

The problem of detecting communities is one of the essential problems in the study of social networks. To devise the algorithms of community detection, one should first define high-quality communities. In fact, there are no agreed methods to measure the quality of the community. In this paper, we consider a novel objective function of this problem. Our goal is to maximize not only the average of the sum of edge weights within communities (i.e., average-case) but also the sum of edge weights within the minimum community (i.e., worst-case). To balance both the average-case and worst-case problems, we introduce a parameter into our objective function and call it the mixed-cased community detection problem. For the worst-case, we devise several approximation algorithms, such as the Greedy, Semi-Sandwich Approximation, and Local Search algorithms. For the average-case, an efficient Terminal-based algorithm is proposed. We prove that the best solution between the average-case and worst-case problems still can provide an approximate guarantee for any mixed-case community detection problem. Moreover, we devise a heuristic algorithm for our problem. Finally, we conduct the experiments in three networks. The experimental results indicate that our proposed methods can form a high-quality community partition. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

The paper proposes a novel objective function for community detection in social networks, aiming to balance the average and worst-case scenarios of edge weight sums within communities. By introducing various approximation algorithms and a heuristic algorithm, high-quality community partitions can be formed in the social networks.