A domain wall (DW) in a ferromagnetic nanowire is composed of elementary topological bulk and edge defects with integer and fractional winding numbers, respectively, whose relative spatial arrangement determines the chirality of the DW. Here we show how we can understand and control the trajectory of DWs in magnetic branched networks, composed of connected nanowires, by considering their fractional elementary topological defects and how they interact with those innate to the network. We first develop a highly reliable mechanism for the injection of a DW of a given chirality into a nanowire and show that its chirality determines which branch the DW follows at a symmetric Y-shaped magnetic junction - the fundamental building block of the network. Using these concepts, we unravel the origin of the one-dimensional nature of magnetization reversal of connected artificial spin ice systems that have been observed in the form of Dirac strings. © 2013 Macmillan Publishers Limited. All rights reserved.