This paper studies uncertain graph data mining and especially investigates the problem of mining frequent subgraph patterns from uncertain graph data. A data model is introduced for representing uncertainties in graphs, and an expected support is employed to evaluate the significance of subgraph patterns. By using the apriori property of expected support, a depth-first search-based mining algorithm is proposed with an efficient method for computing expected supports and a technique for pruning search space, which reduces the number of subgraph isomorphism testings needed by computing expected support from the exponential scale to the linear scale. Experimental results show that the proposed algorithm is 3 to 5 orders of magnitude faster than a na?ve depth-first search algorithm, and is efficient and scalable.