Analysis of a superconducting 1D network (‘ladder’), based on the “J² model”, yields an Ising like expression for the total energy of the network as a function of the loops’ vorticities and the external magnetic field.  This expression includes interaction terms between fluxoids and between them and the external magnetic field.  Competition between these two terms elucidates the mechanism governing the fluxoid arrangement in the network as a function of the field.  In particular, it explains why the first fluxoid always appears in the loop at the network’s center, or next to it, in ladders with an odd or even number of loops, respectively. It is demonstrated that while in ladders with an odd number of loops the fluxoid arrangements are always commensurate to the network symmetry, the symmetry is broken when the loops number is even.