In query based Web search, a significant percentage of user queries are underspecified, most likely by naive users. Collaborative ranking helps the naive user by exploiting the collective expertise. We present a novel algorithmic model inspired by the network flow theory, which constructs a search network based on search engine logs to describe the relationship between the relevant entities in search: queries, documents, and users. This formal model permits the theoretical investigation of the nature of collaborative ranking in more concrete terms, and the learning of the dependence relations among the different entities. FlowRank, an algorithm derived from this model through an analysis of empirical usage patterns, is implemented and evaluated. We empirically show its potential in experiments involving real-world user relevance ratings and a random sample of 1,334 documents and 100 queries from a popular document search engine. Definite improvements over two baseline ranking algorithms for approximately 47% of the queries are reported.