Abstract: Due to the transfer of individuals and changes in individuals' interests, communities are complex networks that evolve over time. We present a community evolution analysis algorithm for dynamic networks with a basis in spectral clustering, so that the evolutionary processes of community structures over time can be revealed. A particular focus is placed upon consideration of current time-snapshot observations and upon community evolution. By employing the stochastic block model and the Dirichlet distribution for modeling, the problem of community evolution is formulated as an optimization problem. Our theoretical proof that the community evolution problem is equivalent to spectral clustering lays the theoretical foundation for adopting a spectral clustering framework-based solution for modeling community evolution. Experimental results on a synthetic data set show that our proposed method is superior to aspectral clustering approach that takes the normalized cut as its objective with regards to accuracy and the detection of the stability of dynamic communities.