Pore networks can be extracted from 3D rock images to accurately predict multi-phase flow properties of rocks by network flow simulation. However, the predicted flow properties may be sensitive to the extracted pore network if it is small, even though its underlying characteristics are representative. Therefore, it is a challenge to investigate the effects on flow properties of microscopic rock features individually and collectively based on small samples. In this article, a new approach is introduced to generate from an initial network a stochastic network of arbitrary size that has the same flow properties as the parent network. Firstly, we characterise the realistic parent network in terms of distributions of the geometrical pore properties and correlations between these properties, as well as the connectivity function describing the detailed network topology. Secondly, to create a stochastic network of arbitrary size, we generate the required number of nodes and bonds with the correlated properties of the original network. The nodes are randomly located in the given network domain and connected by bonds according to the strongest correlation between node and bond properties, while honouring the connectivity function. Thirdly, using a state-of-the-art two-phase flow network model, we demonstrate for two samples that the rock flow properties (capillary pressure, absolute and relative permeability) are preserved in the stochastic networks, in particular, if the latter are larger than the original, or the method reveals that the size of the original sample is not representative. We also show the information that is necessary to reproduce the realistic networks correctly, in particular the connectivity function. This approach forms the basis for the stochastic generation of networks from multiple rock images at different resolutions by combining the relevant statistics from the corresponding networks, which will be presented in a future publication.