Majorana zero modes in a nanowire network*

We study theoretically ways to use physical Majorana zero modes in semiconductor nanowire junctions to build logical Majorana zero-mode states on a network. Employing symmetry arguments, we determine the number of zero modes that can exist on junctions of arbitrary coordination and for various magnetic and spin-orbit field configurations. We use these results to construct a honeycomb network of zero-mode-carrying wires and compute several of its spectral characteristics, such as local and global density of states. We also study ways to perform non-Abelian braiding operations on zero modes supported by the honeycomb network.