The Abstraction and Reasoning Corpus (ARC) aims at benchmarking the performance of general artificial intelligence algorithms. The ARC's focus on broad generalization and few-shot learning has made it impossible to solve using pure machine learning. A more promising approach has been to perform program synthesis within an appropriately designed Domain Specific Language (DSL). However, these too have seen limited success. We propose Abstract Reasoning with Graph Abstractions (ARGA), a new object-centric framework that first represents images using graphs and then performs a constraint-guided search for a correct program in a DSL that is based on the abstracted graph space. Early experiments demonstrates the promise of ARGA in tackling some of the complicated tasks of the ARC rather efficiently, producing programs that are correct and easy to understand.