An approach for overlapping and hierarchical community detection in social networks based on coalition formation game theory

The coalition formation game theory is applied to detect communities.A utility function is proposed and its properties have been examined theoretically.No prior knowledge on number and size of communities is required in our approach.Extensive experiments have been done to evaluate the proposed approach. With greater availability of data and increasing interaction activities taking place on social media, detecting overlapping and hierarchical communities has become an important issue and one that is essential to social media analysis. In this paper, we propose a coalition formation game theory-based approach to identify overlapping and hierarchical communities. We model community detection as a coalition formation game in which individuals in a social network are modelled as rational players aiming to improve the group's utilities by cooperating with other players to form coalitions. Each player is allowed to join multiple coalitions, and those coalitions with fewer players can merge into a larger coalition as long as the merge operation is beneficial to the utilities of the merged coalitions, thus overlapping and hierarchical communities can be revealed simultaneously. The utility function of each coalition is defined as the combination of a gain function and a cost function. The gain function measures the degree of interactions amongst the players inside a coalition, while the cost function instead represents the degree of the interactions between the players of the coalition and the rest of the network. As game theory provides a formal analytical framework with a set of mathematical tools to study the complex interactions among rational players, applying game theory for detecting communities helps to identify communities more rationally. Some desirable properties of the utility function, such as the non-resolution limit and the non-scaling behavior, have been examined theoretically. To solve the issue of pre-setting the number and size for communities and to improve the efficiency of the detection process, we have developed a greedy agglomerative manner to identify communities. Extensive experiments have been conducted on synthetic and real networks to evaluate the effectiveness and efficiency of the proposed approach which can be applied for real world applications.