  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.
