Graph clustering becomes an important problem due to emerging applications involving the web, social networks and bio-informatics. Recently, many such applications generate data in the form of streams. Clustering massive, dynamic graph streams is significantly challenging because of the complex structures of graphs and computational difficulties of continuous data. Meanwhile, a large volume of side information is associated with graphs, which can be of various types. The examples include the properties of users in social network activities, the meta attributes associated with web click graph streams and the location information in mobile communication networks. Such attributes contain extremely useful information and has the potential to improve the clustering process, but are neglected by most recent graph stream mining techniques. In this paper, we define a unified distance measure on both link structures and side attributes for clustering. In addition, we propose a novel optimization framework DMO, which can dynamically optimize the distance metric and make it adapt to the newly received stream data. We further introduce a carefully designed statistics SGS(C) which consume constant storage spaces with the progression of streams. We demonstrate that the statistics maintained are sufficient for the clustering process as well as the distance optimization and can be scalable to massive graphs with side attributes. We will present experiment results to show the advantages of the approach in graph stream clustering with both links and side information over the baselines.