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In the Graph classification context, frequent graph patterns are more used by many researchers as graphs classification features because its significant outcome result in graph classification such as prediction of proteins and molecules, graph data analysis and computation program flows. However, frequent pattern mined becomes non-trivial since the number of patterns is exponential. For this reason graph pattern mining has shifted from finding all frequent subgraphs to obtaining a small subset of frequent subgraphs that are representative, discriminative or significant. The process of finding a subset among all frequent subgraphs is NP-hard and estimation heuristic algorithms used doesn't give optimal solution of subset selected. In this paper we present an approach “Graph Classification based on Top near optimal Co-occurrence Graph patterns of size-k (TCG)”. The approach exploits the submodular property of information gain and special greedily select top co-occurrence subgraphs of size k among frequent subgraphs. Graph classification built on mined co-occurrence subgraphs show the quality of our approach and improvement on accuracy. [ABSTRACT FROM PUBLISHER]