1. A method for diagnosing network performance problems, the method comprising: providing a graph representing a topology of a network comprising first nodes that are classified as providers of a resource, second nodes that are classified as consumers of the resource, and third nodes that are classified as mediators intervening between the providers and the consumers; receiving a report of a performance problem encountered by a given consumer in the network; responsively to the report, tracing at least one input/output (I/O) path through the graph connecting the given consumer to one or more of the providers; and identifying one or more problematic nodes along the at least one I/O path as possible causes of the performance problem.