We introduce a unified graph representation of the Web, which includes both structural and usage information. We model this graph using a simple union of the Web's hyperlink and click graphs. The hyperlink graph expresses link structure among Web pages, while the click graph is a bipartite graph of queries and documents denoting users' searching behavior extracted from a search engine's query log. Our most important motivation is to model in a unified way the two main activities of users on the Web: searching and browsing, and at the same time to analyze the effects of random walks on this new graph. The intuition behind this task is to measure how the combination of link structure and usage data provide additional information to that contained in these structures independently. Our experimental results show that both hyperlink and click graphs have strengths and weaknesses when it comes to using their stationary distribution scores for ranking Web pages. Furthermore, our evaluation indicates that the unified graph always generates consistent and robust scores that follow closely the best result obtained from either individual graph, even when applied to "noisy" data. It is our belief that the unified Web graph has several useful properties for improving current Web document ranking, as well as for generating new rankings of its own. In particular stationary distribution scores derived from the random walks on the combined graph can be used as an indicator of whether structural or usage data are more reliable in different situations.