In order to plan the network construction reasonable and ensure the quality of network service, it is important to measure the Link-bandwidth utilization and get the flow information. One of the methods to monitor network efficiently is based on flow-conservation, and the problem of searching a solution for this method could be deduced to solving weak vertex cover problem, which has been proved NP-hard. So finding an optimum solution for weak vertex cover problem is critical for the network measurement based on flow-conservation. In this paper, we proposed a method using topology matrix to represent the topology graph information and remove the redundant nodes through back tracing the result node set. This method can get a better solution than general greedy algorithm. An example and emulation have been provided to exemplify this method.