Community detection is an important task for social networks, which helps us understand the functional modules on the whole network. Among different community detection methods based on graph structures, modularity-based methods are very popular recently, but suffer a well-known resolution limit problem. This paper connects modularity-based methods with correlation analysis by subtly reformatting their math formulas and investigates how to fully make use of correlation analysis to change the objective function of modularity-based methods, which provides a more natural and effective way to solve the resolution limit problem. In addition, a novel theoretical analysis on the upper bound of different objective functions helps us understand their bias to different community sizes, and experiments are conducted on both real life and simulated data to validate our findings.