The Neural Networks N.Ns. are.parts of the artificial intelligence considered in computer science domain which appear as a result of the fast evolution in computers especially in the last two decades. The N.Ns. have been applied in several directions like image processing, geographical survey, financial forecasting, medicine etc., as well as, communications and routing which is the concept of this thesis. The N.N. is applied to establish a communication path between two nodes, such that the proposed path is more appropriate than the others under the condition that the total congestion of the N.N. is minimized to obtain optimal flow of information through the N. W. The proposed metric that used to measure the distance is the number of hops, such that, if a direct path exist between two nodes will be better than including third node, the use of this metric provide a very good result in computer simulation test. Although, alternative metric was also tested, such as the cost of the path between two nodes, but unfortunatly the results were very weak and inefficient, which means that the N.N. is still under evolution and till now can not be applied for all applications, and this is the case in most modern sciences which start in specific frame and progress with effort of scientist through time. In addition, some classical methods for measuring shortest path are used, ' such as Dijkstra and modified Dijkstra, which act's as a data preparation phase and considered as a supporting tool for the proposed N.N. system. These methods proved their efficiency through computer simulation test, in which merging the classical and N.N. is achieved to obtain a communication technique ensure/shortest, as well as, best paths selection.