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The goal of this paper is to generate insights about the differences between graph-based and logic-based approaches to multi-relational data mining by performing a case study of the graph-based system, Subdue and the inductive logic programming system, CProgol. We identify three key factors for comparing graph-based and logic-based multi-relational data mining; namely, the ability to discover structurally large concepts, the ability to discover semantically complicated concepts and the ability to effectively utilize background knowledge. We perform an experimental comparison of Subdue and CProgol on the Mutagenesis domain and various artificially generated Bongard problems. Experimental results indicate that Subdue can significantly outperform CProgol while discovering structurally large multi-relational concepts. It is also observed that CProgol is better at learning semantically complicated concepts and it tends to use background knowledge more effectively than Subdue.