In this paper, we focus on dense graph streams, which can be generated in various applications ranging from sensor networks to social networks, from bio-informatics to chemical informatics. We also investigate the problem of effectively and efficiently mining frequent patterns from such streaming data, in the targeted case of dealing with limited memory environments so that disk support is required. This setting occurs frequently (e.g., in mobile applications/systems) and is gaining momentum even in advanced computational settings where social networks are the main representative. Inspired by this problem, we propose (i) a specialized data structure called DSMatrix, which captures important data from dense graph streams onto the disk directly and (ii) stream mining algorithms that make use of such structure in order to mine frequent patterns effectively and efficiently. Experimental results clearly confirm the benefits of our approach.