An artificial neural network model, capable of processing general types of graph structured data, has recently been proposed. This paper applies the new model to the computation of customised page ranks problem in the World Wide Web. The class of customised page ranks that can be implemented in this way is very general and easy because the neural network model is learned by examples. Some preliminary experimental findings show that the model generalizes well over unseen web pages, and hence, may be suitable for the task of page rank computation on a large web graph.