The variant graph is a new, hybrid algorithm that combines the strengths of established global grain graph and local neighbor level voting approaches, while alleviating their shortcomings, to reconstruct parent grains from orientation maps of partially or fully phase-transformed microstructures. The variant graph algorithm is versatile and is capable of reconstructing transformation microstructures from any parent-child combination by clustering together child grains based on a common parent orientation variant. The main advantage of the variant graph over the grain graph is its inherent ability to more accurately detect prior austenite grain boundaries. A critical examination of Markovian clustering and neighbor level voting as methods to reconstruct prior austenite orientations is first conducted. Following this, the performance of the variant graph algorithm is showcased by reconstructing the prior austenite grains and boundaries from an example low-carbon lath martensite steel microstructure. Programmatic extensions to the variant graph algorithm for specific morphological conditions and the merging of variants with small mutual disorientation angles are also proposed. The accuracy of the reconstruction and the computational performance of the variant graph algorithm is either on-par or outperforms alternate methods for parent grain reconstruction. The variant graph algorithm is implemented as a new addition to the functionalities for phase transformation analysis in MTEX 5.8 and is freely available for download by the community.