A network epidemic model for cholera and other diseases that can be transmitted via the environment is developed by adapting the Miller model to include the environment. The person-to-person contacts are modeled by a random contact network, and the contagious environment is modeled by an external node that connects to every individual. The dynamics of our model show excellent agreement with stochastic simulations. The basic reproduction number R0 is computed, and on a Poisson network shown to be the sum of the basic reproduction numbers of the person-to-person and person-to-water-to-person transmission pathways, as in the homogeneous mixing limit. How- ever, on other networks, R0 depends nonlinearly on the transmission along the two pathways. Type reproduction numbers are computed and quantify measures to control cholera.