We consider the estimation of the entropy of a discrete dynamical system by using a symbolic image that is a directed graph constructed by means of a finite covering of phase space. Trajectories of the system are coded by paths on the graph. Flows on а symbolic image approximate invariant measures of the system. The maximal metric entropy of a symbolic image is estimated by the logarithm of the maximal eigenvalue of the symbolic image adjacency matrix. There is the flow on which this entropy is achieved. The invariant measure of the maximal entropy is estimated by using this flow.