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This paper proposes neural networks based graph coloring technique to assign Physical Cell Identities throughout the self organized 3GPP Long Term Evolution Networks. PCIs are allocated such that no two cells in the vicinity of each other or with a common neighbor get the same identity. Efficiency of proposed methodology resides in the fact that minimum number of identities is utilized in the network wise assignment. Simulations are performed on a very large scale network, where initially all the cells are without any PCIs assigned. Results of simulations are demonstrated to analyze the performance of the proposed technique.