Van der Waals (vdW) epitaxial double heterostructures have been fabricated by vdW epitaxy of InAs nanostructures on both sides of graphene. InAs nanostructures diametrically form on/underneath graphene exclusively along As-polar direction, indicating polarity inversion of the double heterostructures. First-principles and density functional calculations demonstrate how and why InAs easily form to be double heterostructures with polarity inversion.