We generate the network model equivalents of four samples of Fontainebleau sandstone obtained from the analysis of microtomographic images. We present the measured distributions of flow-relevant geometric and topological properties of the pore space. We generate via bond dilution from a regular lattice, stochastic network models with identical geometric (pore-size, throat-size) and topological (coordination number distribution) properties. We then simulate the two-phase flow properties directly on the network model and the stochastic equivalent for each sample. The simulations on the stochastic networks are found to provide a poor representation of the results on the direct network equivalents. We find that the description of the network topology is particularly crucial in accurately predicting the residual phase saturations. We also find it necessary to introduce into the stochastic network geometry both extended pore-pore correlations and local pore-throat correlations to obtain good agreement with flow properties on the rock-equivalent network.