Abstarct: Nowadays, nonlinear loads are vastly common in power networks. As a result, levels of harmonics are increased drastically. Power electric tools, switching devices and nonlinear loads can be considered as the main causes for this problem. The application of this equipment in power systems can be caused currents distortion existing in the network. These distorted currents can cause voltage distortion throughout the power system even when supplied with a purely sinusoidal voltage. Distorted currents and voltages cause degrading in power quality. There are several ways to ameliorate this condition. Among them, passive filters are known as economical and efficient ways. In this thesis, for the first time we established a new method for devising passive filters by utilizing graph algorithm. The optimum positions for filters can be found by the purposed method. For fast convergence, four kinds of movements among the buses are devised. The purposes of filter design in the network are decreasing cost of the filters, loss of the network and total harmonic distortion of voltage and improving voltage profile. We applied this method on 30-bus IEEE system. The results showed this method can be an outstanding method for devising filters for power networks.