We present a new stochastic process, called as Social Diffusion Process (SDP), to address the graph modeling. Based on this model, we derive a graph evolution algorithm and a series of graph-based approaches to solve machine learning problems, including clustering and semi-supervised learning. SDP can be viewed as a special case of Matthew effect, which is a general phenomenon in nature and societies. We use social event as a metaphor of the intrinsic stochastic process for broad range of data. We evaluate our approaches in a large number of frequently used datasets and compare our approaches to other state-of-the-art techniques. Results show that our algorithm outperforms the existing methods in most cases. We also applying our algorithm into the functionality analysis of microRNA and discover biologically interesting cliques. Due to the broad availability of graph-based data, our new model and algorithm potentially have applications in wide range.