Failure indexing is an essential step in parallel debugging, and many research efforts have been devoted to failure indexing in recent years. However, state-of-the-art failure indexing techniques still suffer from the key issues of improperly characterizing the distinct failure properties and poor clustering performance arising from sensitivity to outliers and noise. To address these issues, this paper proposes GREClue, a novel failure indexing approach with Graph-based failure Representation and Entropy-based deep Clustering. GREClue overcomes the issues in a synergistic way. To begin with, GREClue designs the failure property graph (FPG), a new graph representation that effectively contains property information and runtime information of failures. On top of FPG, GREClue further consists of an entropy-based deep clustering component, which can deliver satisfactory clustering performance. An extensive evaluation of GREClue on the widely used Defects4J-Multifault and SIR datasets shows that compared to the state-of-the-art failure indexing method, GREClue improves both the performance of estimating the number of faults and the clustering effectiveness by 10% to 41%. In addition, it has also been shown that GREClue can effectively facilitate parallel debugging. Overall, GREClue is promising for assisting the tedious and time-consuming debugging process.