In the current era of Big data, high volumes of valuable data can be generated at a high velocity from high-varieties of data sources in various real-life applications ranging from sensor networks to social networks, from bio-informatics to chemical informatics. In addition, Big data are also available in business, education, engineering, finance, healthcare, scientific, telecommunication, and transportation domains. A collection of these data can be viewed as a big dynamic graph structure. Embedded in them are implicit, previously unknown, and potentially useful knowledge. Consequently, efficient knowledge discovery algorithms for mining frequent subgraphs from these dynamic streaming graph structured data are in demand. On the one hand, some existing algorithms discover collections of frequently co-occurring edges, which may be disjoint. On the other hand, some other existing algorithms discover frequent subgraphs by requiring very large memory space. With high volumes of Big data, available memory space may be limited. To discover collections of frequently co-occurring connected edges, we present in this paper two efficient algorithms that require small memory space. Evaluation results show the efficiency of our edge-based algorithms in mining frequent subgraphs from graph streams.