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We propose a technique for evaluating the statistical significance of frequent subgraphs in a database. A graph is represented by a feature vector that is a histogram over a set of basis elements. The set of basis elements is chosen based on domain knowledge and consists generally of vertices, edges, or small graphs. A given subgraph is transformed to a feature vector and the significance of the subgraph is computed by considering the significance of occurrence of the corresponding vector. The probability of occurrence of the vector in a random vector is computed based on the prior probability of the basis elements. This is then used to obtain a probability distribution on the support of the vector in a database of random vectors. The statistical significance of the vector/subgraph is then defined as the p-value of its observed support. We develop efficient methods for computing p-values and lower bounds. A simplified model is further proposed to improve the efficiency. We also address the problem of feature vector mining, a generalization of item- set mining where counts are associated with items and the goal is to find significant sub-vectors. We present an algorithm that explores closed frequent sub-vectors to find significant ones. Experimental results show that the proposed techniques are effective, efficient, and useful for ranking frequent subgraphs by their statistical significance.