With an exponentially growing number of graphs from disparate repositories, there is a strong need to analyze a graph database containing an extensive collection of small- or medium-sized data graphs (e.g., chemical compounds). Although subgraph enumeration and subgraph mining have been proposed to bring insights into a graph database by a set of subgraph structures, they often end up with similar or homogenous topologies, which is undesirable in many graph applications. To address this limitation, we propose the Top-k Edge-Diversified Patterns Discovery problem to retrieve a set of subgraphs that cover the maximum number of edges in a database. To efficiently process such query, we present a generic and extensible framework called Ted which achieves a guaranteed approximation ratio to the optimal result. Two optimization strategies are further developed to improve the performance. Experimental studies on real-world datasets demonstrate the superiority of Ted to traditional techniques.