In recent years, spectral clustering method has gained attentions because of its superior performance compared to other traditional clustering algorithms such as K-means algorithm. The existing spectral clustering algorithms are all off-line algorithms, i.e., they can not incrementally update the clustering result given a small change of the data set. However, the capability of incrementally updating is essential to some applications such as real time monitoring of the evolving communities of websphere or blogsphere. Unlike traditional stream data, these applications require incremental algorithms to handle not only insertion/deletion of data points but also similarity changes between existing items. This paper extends the standard spectral clustering to such evolving data by introducing the incidence vector/matrix to represent two kinds of dynamics in the same framework and by incrementally updating the eigenvalue system. Our incremental algorithm, initialized by a standard spectral...