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

Ideal Relative Flow Distribution on Directed Network