Summary: Phantom chain MC simulations have been performed for realistically sized systems of polymer chains filled with solid nanoparticles. The results of the simulations and simple theoretical considerations are used to rationalize a number of parameters relevant to the characterization of these systems. Even when the average number of nanoparticles in contact with a chain is very small (much less than unity), the nanoparticles are nodes of highly interconnected transient networks bridged by the polymer chains.