The time characteristics of a linear network in the brain are obtained by the method of the time partition function, which is analogous to a grand partition function or a distribution function in statistical mechanics. The analogy between the average density in a many-particle system and the reciprocal of the frequency in a network is shown. By this method, the frequency distribution functions are obtained with respect to a network composed of two layers, the network used in information retrieval and the network generating a brain wave.