Wireless sensor networks are ad-hoc networks that operate with limited capacity and energy. In wireless sensor networks, it may be desirable to monitor the traffic on the network by checking the links for the security of the system. For such a scenario, the vertex cover problem, which is the well-known problem in the graph theory, can be used. The problem is covering of links on the graph by selecting the minimum number of nodes. Thus, all connections on the network can be controlled using as few devices as possible. Self-stabilizing algorithms are algorithms that stabilize the system without external intervention from a random initial state. At this point, the system guarantees a stabilization after a limited time against possible faults. In this study evaluation of vertex cover algorithms for fault tolerant link monitoring in wireless sensor network is made and it is shown that Kiniwa's algorithm performs better than the other algorithms.