Summary form only given, as follows. A neural network computation algorithm is introduced to solve the optimal traffic routing in a general N-node communication network. The algorithm chooses multilink paths for node-to-node traffic which minimize a certain cost function (e.g. expected delay). Unlike the algorithm introduced earlier in this area, the knowledge about the number of links (hops) between each origin-destination pair is not required by the algorithm, therefore it can be applied to a more general network. The neural network structure for implementing the algorithm is a modification of the one used by the traveling salesman algorithm. Computer simulations in a nine-node grid network show that the algorithm performs well.<>