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Graph matching algorithms attempt to find the best correspondence between the nodes of two networks. These techniques have been used to match individual neurons in nanoscale connectomes-in particular, to find pairings of neurons across hemispheres. However, since graph matching techniques deal with two isolated networks, they have only utilized the ipsilateral (same hemisphere) subgraphs when performing the matching. Here, we present a modification to a state-of-the-art graph matching algorithm that allows it to solve what we call the bisected graph matching problem. This modification allows us to leverage the connections between the brain hemispheres when predicting neuron pairs. Via simulations and experiments on real connectome datasets, we show that this approach improves matching accuracy when sufficient edge correlation is present between the contralateral (between hemisphere) subgraphs. We also show how matching accuracy can be further improved by combining our approach with previously proposed extensions to graph matching, which utilize edge types and previously known neuron pairings. We expect that our proposed method will improve future endeavors to accurately match neurons across hemispheres in connectomes, and be useful in other applications where the bisected graph matching problem arises., (© 2022 Massachusetts Institute of Technology.)