Universal aspects of inhomogeneous transport was studied in natural Josephson junction networks. The weak link networks of polycrystalline high-Tc superconductors were found perfectly suitable for quantitative investigation of cluster growth phenomena in percolation (or fractal) networks. We report the experimental results of our studies of I-V characteristics of the two high-Tc families, YBCO and BSCCO. The onset of dissipation, represented by these characteristics, is interpreted as a critical phenomenon, i.e., as a current-induced phase transition. The cluster growth which underlies this phase transition is analyzed by the use of an appropriate model. The model links the non- Ohmic weak link network with classical Ohmic percolation networks (e.g., random resistor network). As a result, we were able to determine the values of appropriate dynamical exponents (exponent t with high precision, t equals 2 +/- 0.1, and exponent s approximately, s approximately equals 0.7), as well as to assign the dissipative ranges inside which the corresponding cluster dynamics takes place. It is therefore concluded that the high-Tc weak link networks represent a natural mesoscopic-scale system convenient for systematic investigation of the transport critical phenomena.