The limit range and operation boundary of the multi-source and multi-sink network are obtained. Firstly, the critical flow is defined. The maximum flow and blocking flow in existing researches are parts of the critical flow. Then, all critical flows of the multi-source and multi-sink network are obtained for the first time and plotted as a CF curve. The CF curve completely describeds the limit range of the network transmission flow capacity, where the maximum flow is located at its highest point and the minimum flow is located at its lowest point. The critical flow is also used to determine the network operational boundary, inside which are feasible flows, and outside which are unfeasible flows. The mathematical definitions and solutions method of critical flow, CF curve and operational boundary of the multi-source and multi-sink network are proposed. Finally, the possible applications of the critical flow curve and the operational boundary in planning and operation fields are demonstrated. Since most real networks are the multi-source multi-sink networks, so the proposal of critical flow curve and operation boundary can help us know the full limit range of network operation.