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This study deals with the localisation of all nodes in a network, also called as network localisation, based on pairwise distance measurements. The case of a fully connected network is considered, where `fully connected` refers to that within the whole network every pair of nodes directly connect to each other, thus their pairwise distance can be measured and available. For the localisation of such a network, the multi-dimensional scaling (MDS) algorithm can provide a relative localisation solution, but only a coarse solution when there are measurement errors. To bridge the gap in the localisation performance between the MDS-based and optimum network localisation, the authors propose an efficient subsequent refinement, that is, the iterative least square (LS)/weighted least square (WLS) refinement for the widely existing independent zero-mean Gaussian measurement errors. Analysis and simulation study show that with sufficiently small measurement errors the proposed improved network localisation scheme can achieve, in very limited iterations, the LS/WLS solution, which exhibits the localisation performance the same as the Cramer-Rao lower bound. The authors also extend the proposed refinement to the absolute localisation case with sufficient position-known anchors that are fully and directly connected to all sensors of the network.