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This paper compares the solutions obtained by various methods in the literature for sensor network localization based on connectivity. The deficiencies of some of those solutions are discussed. It is argued that the actual problem should be represented as an optimization problem with both convex and non-convex constraints. A new method is proposed which utilizes multi-dimensional scaling (MDS) to provide an initial solution on the location of the unknown nodes and then searches for a solution to satisfy all the constraints of the problem. The final solution can reach the most suitable configuration of the unknown nodes because all the information on the constraints (convex and non-convex) related to connectivity will have been used. Compared with other constraint models that only consider the nodes that have connections, this method considers not only the connection constraints, but also the disconnection constraints. Simulation results have shown that better solution can be obtained through the use of this method when compared with those produced by other methods.