This chapter provides a rigorous theoretical foundation for Ideal Flow Networks (IFN) by connecting the observed behavior of a random walk to the mathematical framework of a Discrete-Time Markov Chain (DTMC). We demonstrate that the cumulative movement of agents on a strongly connected network, when appropriately normalized, converges to a stable and unique relative flow distribution. This asymptotic pattern, defined as the Ideal Flow matrix ( \(\mathsf {F}\) ), is shown to be an intrinsic property of the network’s topology. The chapter formalizes this convergence by proving that the Ideal Flow is the direct result of the DTMC’s unique stationary distribution. A key finding is that the assumption of a uniform random walk is not arbitrary; it represents the most unbiased, maximum entropy state of the system, a property that holds if and only if the corresponding transition probability matrix is a row-steady matrix.