Whereas data mining in structured data focuses on frequent data values, in semi-structured and graph data the emphasis is on frequent labels and common topologies. Here, the structure of the data is just as important as its content. We study the problem of discovering typical patterns of graph data. The discovered patterns can be useful for many applications, including: compact representation of source information and a road-map for browsing and querying information sources. Difficulties arise in the discovery task from the complexity of some of the required sub-tasks, such as sub-graph isomorphism. This paper proposes a new algorithm for mining graph data, based on a novel definition of support. Empirical evidence shows practical, as well as theoretical, advantages of our approach.