Recent developments in the area of neural networks provided new models which are capable of processing general types of graph structures. Neural networks are well-known for their generalization capabilities. This paper explores the idea of applying a novel neural network model to a web graph to compute an adaptive ranking of pages. Some early experimental results indicate that the new neural network models generalize exceptionally well when trained on a relatively small number of pages. Categories and Subject Descriptors: E.1 Data Structures: Graphs and networks. H.3.3.b Information Search and Retrieval: Information Filtering. I.2.6 Learning: Connectionism and Neural Nets. General Terms: Algorithm, Experimentation