For pt.IV see abstr. A67969 of 1973. Gas-phase fluxes, with and without additional surface flow, have been calculated for random, isotropic, two-dimensional and three-dimensional networks comprising a wide range of connectivities. A set of distribution functions which have previously been studied by the authors in parallel (P) and serial (S) models was used. Evidence for the importance of connectivity is augmented by these results. The intermediate status of the network model between the P and S models is confirmed. However when surface flow is present the surface-flow structure factor ks, but not the total flux, can be anomalous in this respect.