Multi-relational data mining (MRDM) is concerned with discovering hidden patterns from multiple tables in a relational database. One of the most commonly addressed tasks in MRDM is concept discovery in which the problem is inducing logical definitions of a specific relation, called target relation, in terms of other relations, called background knowledge. Inductive Logic Programming-based and graph-based approaches are two main competitors in this research. In this paper, we aim to introduce concept discovery problem and compare state-of-the-art methods in graph-based concept discovery by means of data representation, search method, and concept descriptor evaluation mechanism.