Document coherence describes how much sense text makes in terms of its logical organisation and discourse flow. Even though coherence is a relatively difficult notion to quantify precisely, it can be approximated automatically. This type of coherence modelling is not only interesting in itself, but also useful for a number of other text processing tasks, including Information Retrieval (IR), where adjusting the ranking of documents according to both their relevance and their coherence has been shown to increase retrieval effectiveness. The state of the art in unsupervised coherence modelling represents documents as bipartite graphs of sentences and discourse entities, and then projects these bipartite graphs into one–mode undirected graphs. However, one–mode projections may incur significant loss of the information present in the original bipartite structure. To address this we present three novel graph metrics that compute document coherence on the original bipartite graph of sentences and entities. Evaluation on standard settings shows that: (i) one of our coherence metrics beats the state of the art in terms of coherence accuracy; and (ii) all three of our coherence metrics improve retrieval effectiveness because, as closer analysis reveals, they capture aspects of document quality that go undetected by both keyword-based standard ranking and by spam filtering. This work contributes document coherence metrics that are theoretically principled, parameter-free, and useful to IR.