6. A method comprising receiving an initial query; selecting one or more additional queries relating to the initial query; determining a respective utility measure for each of the one or more additional queries, wherein the utility measure represents a likelihood that a respective additional query would be a final query submitted in a query session, wherein the utility measure is determined from a query graph that represents one or more query refinements from the initial query to one of the additional queries, wherein each particular query refinement in the graph has a respective associated weight that represents a likelihood of the particular query refinement being submitted in the query session; selecting an additional query from the one or more additional queries having a highest utility measure; and providing the selected additional query to a client device to be displayed along with search results associated with the initial query.
6. A method comprising receiving an initial query; selecting one or more additional queries relating to the initial query; determining a respective utility measure for each of the one or more additional queries, wherein the utility measure represents a likelihood that a respective additional query would be a final query submitted in a query session, wherein the utility measure is determined from a query graph that represents one or more query refinements from the initial query to one of the additional queries, wherein each particular query refinement in the graph has a respective associated weight that represents a likelihood of the particular query refinement being submitted in the query session; selecting an additional query from the one or more additional queries having a highest utility measure; and providing the selected additional query to a client device to be displayed along with search results associated with the initial query. 10. The method of claim 6 , wherein the initial query includes one or more query terms.