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; identifying one or more problematic nodes along the at least one I/O path as possible causes of the performance problem; tracing a further I/O path through the graph connecting another consumer to the providers and crossing the at least one I/O path at one of the problematic nodes after identifying one or more problematic nodes along the at least one I/O path; and identifying one or more further problematic nodes along the further I/O path as a possible cause of the performance problem, wherein providing the graph comprises identifying physical and logical links between the nodes, and wherein tracing the at least one I/O path comprises building the at least one I/O path in accordance with the logical links.