Abstract: An improved method to research simulation graph of the bidirectional double-loop networks G（N；±1，±s） is presented based on Cartesian coordinates which has been creatively used.Based on these researches，the definition of the best bidirectional double-loop networks G（N；±1，±s） is given whose diameter and average diameter are both optimal and the relationship is also studied between diameter and step s.At last，the simulation of the graph of the best bidirectional double-loop networks G（N；±1，±s） is given for any given diameter.Compared with L-shaped tile simulation which can not be used in the bidirectional double-loop networks directly，this method improves the research level of the bidirectional double-loop networks greatly，and has not been reported in existing documents.

摘要： 创造性地将直角坐标系引入无向双环网络的研究，通过直角坐标系，系统研究无向双环网络G（N；±1，±s）的仿真图形，提出最优无向双环网络BestG（N；±1，±s）（直径、平均直径均达到下界）的构造方法并研究步长s和其直径之间的关系。与传统L型瓦方法在无向双环网络研究中相比，该方法克服其不足，大大提升了无向双环网络的研究水平，相关研究在国内外文献中尚未见到。