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If only one bus in a multi-island power system is energized, the voltages at buses in the same island as the energized bus are non-zero, while the voltages at the buses in other islands are all zero. Based on this idea a network topology method by solving the equations whose coefficient matrix is adjacency matrix is presented. The elements of the coefficient matrix and the right-hand vector of the equations are logic variables, so the equations can be solved directly by Gauss elimination in logic operation form without iteration. All these characteristics efficiently decrease the computer time. The using of sparse matrix method, sparse vector method and optimally ordering can also greatly increase the speed of the proposed method. A practical network being analyzed by the proposed method is presented, and the results prove the effectiveness of the proposed method.