A large amount of research has recently focused on the graph structure (or link structure) of the World Wide Web. This structure has proven to be extremely useful for improving the performance of search engines and other tools for navigating the web. However, since the graphs in these scenarios involve hundreds of millions of nodes and even more edges, highly space-efficient data structures are needed to fit the data in memory. A first step in this direction was done by the DEC Connectivity Server, which stores the graph in compressed form. In this paper, we describe techniques for compressing the graph structure of the web, and give experimental results of a prototype implementation. We attempt to exploit a variety of different sources of compressibility of these graphs and of the associated set of URLs in order to obtain good compression performance on a large web graph.