Graph classification is a difficult task because finding a good feature representation for graphs is challenging. Existing methods use topological metrics or local subgraphs as features, but the time complexity for finding discriminatory subgraphs or computing some of the crucial topological metrics (such as diameter and shortest path) is high, so existing methods do not scale well when the graphs to be classified are large. Another issue of graph classification is that the number of distinct graphs for each class that are available for training a classification model is generally limited. Such scarcity of graph data resources yields models that have much fewer instances than the model parameters, which leads to poor classification performance. In this work, we propose a novel approach for solving graph classification by using two alternative graph representations: the bag of vertices and the bag of partitions. For the first representation, we use representation learning-based node features and for the second, we use traditional metric-based features. Our experiments with 43 real-life graphs from seven different domains show that the bag representation of a graph improves the performance of graph classification significantly. We have shown 4–75% improvement on the vertex-based and 4–36% improvement on partition-based approach over the existing best methods. Besides, our vertex and partition multi-instance methods are on average 75 and 11 times faster in feature construction time than the current best, respectively.