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How does a social network evolve? Sociologists have studied this question since 1930s. Some famous sociologists (for example, Scott Feld) concluded that a social network is composed of superposed cliques of different sizes, and a social network evolves in the form of clique superposition. However, sociologists didn't verify the theory in large scale data due to lack of computing ability. Motivated by this challenge, incorporated with the theory, we propose a Clique-superposition model for social networks. This model generates undirected weighted networks which obey earlier reported patterns and the new patterns observed in our study. The main contributions of this study include the following: (a) we discover a number of new patterns in undirected weighted social networks based on three large real world data sets, (b) we study the principle of social network evolution and propose a Clique-superposition model for social networks following our intuition, (c) we conduct extensive experiments to demonstrate that our model can generate networks with observed patterns, old and new.