Before revision:  We model the information propagation on a brain graph by the generalized Markov system associated to a new edge transition matrix. The volume entropy is estimated by the stationary equation of the generalized Markov system.
After revision:  We model the information propagation on a brain graph by the generalized Markov system associated to the weighted edge-transition matrix. We estimate the volume entropy using the stationary equation of the generalized Markov system.