  In this paper we propose a new concept to prioritize the importance of a link
in a directed network graph based on an ideal flow distribution. An ideal flow
is the infinite limit of relative aggregated count of random walk agents'
trajectories on a network graph distributed over space and time. The standard
ideal flow, which is uniformly distributed flow over space and time, maximize
the entropy for the utilization of a network. We show that the simulated
trajectories of random walk agents would form an ideal relative flow
distribution is converged to stationary values. This implies that ideal flow
matrix depends only on the network structure. Ideal flow matrix is invariant to
scalar multiplication and remarkably it is always premagic. Demonstration of
ideal flow to the real world network was fitted into Sioux Falls transportation
network.
