Abstract: The modern city communication network is optimized according to the principle of  the graph theory and the fuzzy set.It will establish a model with the  shortest distance,the lowest expense,the highest network reliability to guarantee certain restraint condition,such as network connectivity and radiation movement.It aims at getting the approximate optimal solution of erecting the communication network.This article studies some factors in the network construction that the boundary is undistinguishable.It has established the fuzzy minimal spanning tree model,and quoted the classical algorithm of building the minimal spanning tree.It is simple,practical,quick for real-time operation.It is applicable in the construction of the modern city network.The algorithm has proven its superiority after the procedure test.

Key words: communications network, graph theory, fuzzy set, minimal spanning tree, Kruskal&rsquo, s algorithm