Finding a Friendly Community in Social Networks Considering Bad Relationships

Abstract

Community detection in social networks is one of the most active problems with lots of applications. Most of the existing works on the problem have focused on detecting the community considering only the closeness between community members. In the real world, however, it is also important to consider bad relationships between members. In this paper, we propose a new variant of the community detection problem, called friendly community search. In the proposed problem, for a given graph, we aim to not only find a densely connected subgraph that contains a given set of query nodes but also minimizes the number of nodes involved in bad relationships in the subgraph. We prove that is Non-deterministic Polynomial-time hard (NP-hard), and develop two novel algorithms, called Greedy and SteinerSwap that return the near optimal solutions. Experimental results show that two proposed algorithms outperform the algorithm adapted from an existing algorithm for the optimal quasi-clique problem.