To support rapid repair of pipe accidents and improve the reliability of water distribution networks (WDNs)

an approach of finding all valve closing schemes for a network in one time and evaluating the importance of valves and pipes was studied. By using graph theory and Warshall Algorithm (WA)

redundant valves which cannot block the flow of water and segments (i.e. the smallest isolation portion of water supply networks formed by closing a subset of valves) were identified to build valve-segment models. Using the models

unnecessary closing valves (downstream valves of isolated segments) and unintended segments which are parts of the network disconnected from water source(s) as the secondary effect of segment isolation were then analyzed. After excluding the unnecessary closing valves from the boundary valves of isolated segments

all valve closing schemes were formed which can meet a single or multiple pipe accidents. Also

the extension of valve closing schemes was analyzed when a valve malfunction occurs. Additionally

to improve the reliability of valves and assist scientific pipe patrol and valve maintenance

the importance of segments (pipes) and valves was evaluated by using the total demand shortfall coming from isolated segments and their unintended segments while key valves and segments were identified. The application in Tianjin water networks illustrates that segments provide a shortcut to build all valve closing schemes and analyze the importance of pipes and valves for WDNs.