This paper proposes a network model of multilaterally equilibrium exchange rates. The model introduces a topological component into the exchange rate analysis, consistently taking into account simultaneous higher-order interactions among all currencies. The paper defines the currency demand indicator. On its base, it derives a multilateral exchange rate network, finds its dynamically stationary position, and identifies the multilaterally equilibrium levels of bilateral exchanges rates. Potentially, the model can be developed further to calculate the deviations of the observed bilateral exchange rates from their multilaterally equilibrium levels, which can be interpreted as their over- or undervaluation. For illustration, the model is applied to daily 1995-2016 exchange rates among 130 currencies sourced from the Thomson Reuters Datastream.