  The resistive transition of granular high-T$_c$ superconductors,
characterized by either weak (YBCO-like) or strong (MgB$_2$-like) links, occurs
through a series of avalanche-type current density rearrangements. These
rearrangements correspond to the creation of resistive layers, crossing the
whole specimen approximately orthogonal to the current density direction, due
to the simultaneous transition of a large number of weak-links or grains. The
present work shows that exact solution of the Kirchhoff equations for strongly
and weakly linked networks of nonlinear resistors, with Josephson junction
characteristics, yield the subsequent formation of resistive layers within the
superconductive matrix as temperature increases. Furthermore, the voltage noise
observed at the transition is related to the resistive layer formation process.
The noise intensity is estimated from the superposition of voltage drop
elementary events related to the subsequent resistive layers. At the end of the
transition, the layers mix-up, the step amplitude decreases and the resistance
curve smoothes. This results in the suppression of noise, as experimentally
found. Remarkably, a scaling law for the noise intensity with the network size
is argued. It allows to extend the results to networks with arbitrary size and,
thus, to real specimens.
