生成回路網の力学的考察

抄録

It is important for fundamental studies of networks that the generating networks whose connection is systematically generated in a certain order, be considered. Among the above networks there are those which bring about some change of connection structure in its generation, such as, electric networks connected gradually and nerve, communication and traffic networks. Now, network complexity defined by the number of paths in the network graphs may be regarded as position variables in dynamics. Therefore, corresponding to Newtoniany mechanics, generation velocity and generation acceleration are introduced ; generation force can be introduced as a superficial causal quantity. On the basis of this plan, the connection structure of generating networks can be expressed analytically, though approximately. That is to say, by establishing the order of generation appropriately, it is explained that some generation patterns of networks can be classified by the form of the generation force. In the case where a number of networks are independently generated without mutual connections, the fundamental characters of the generating networks are obtained in correspondence with the principle of superposition and parallel displacement in dynamics. On the other hand, in generating networks which have simple mutual connections, it is shown for the interpretation that generation forces are divided into two major parts ; namely, one which exists when each networks is respectively independent and the other which is produced by interaction caused by the connections of each networks.