Signed networks are ubiquitous in the real world. It is of great significance to study the problem of community detection in signed networks. In general, the behaviors of nodes in a signed network are rational, which coincide with the players in the theory of game that can be used to model the process of the community formation. Unlike unsigned networks, signed networks include both positive and negative edges, representing the relationship of friends and foes respectively. In the process of community formation, nodes usually choose to be in the same community with friends and between different communities with enemies. Based on this idea, we proposed a game theory model to address the problem of community detection in signed networks. Taking nodes as players, we build a gain function based on the numbers of positive edges and negative edges inside and outside a community, and prove the existence of Nash equilibrium point. In this way, when the game reaches the Nash equilibrium state, the optimal strategy space for all nodes is the result of the final community division. To systematically investigate the performance of our method, elaborated experiments on both synthetic networks and real-world networks are conducted. Experimental results demonstrate that our method is not only more accurate than other existing algorithms, but also more robust to noise.

Detecting community structures and analyzing temporal evolution in dynamic networks are challenging tasks to explore the inherent characteristics of the complex networks. In this paper, we propose a semi-supervised evolutionary clustering model based on symmetric nonnegative matrix factorization to detect communities in dynamic networks, named sEC-SNMF. We use the results of community partition at the previous time step as the priori information to modify the current network topology, then smooth-out the evolution of the communities and reduce the impact of noise. Furthermore, we introduce a community transition probability matrix to track and analyze the temporal evolutions. Different from previous algorithms, our approach does not need to know the number of communities in advance and can deal with the situation in which the number of communities and nodes varies over time. Extensive experiments on synthetic datasets demonstrate that the proposed method is competitive and has a superior performance.