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We have developed analytical and numerical methods to study the transport of noninteracting particles in large networks consisting of -dimensional containers with radii linked together by tubes of length and radii where . Tubes may join directly with each other, forming junctions. It is possible that some links are absent. Instead of solving the diffusion equation for the full problem we formulated an approach that is computationally more efficient. We derived a set of rate equations that govern the time dependence of the number of particles in each container, . In such a way the complicated transport problem is reduced to a set of first-order integro-differential equations in time, which can be solved efficiently by the algorithm presented here. The workings of the method have been demonstrated on a couple of examples: networks involving three, four, and seven …