This paper introduces a new trade model type. It combines the gravity model, well-known in international economics, with network theory. With this approach, complicated trade networks can be algebraically solved in form of systems of linear (differential) equations. Business cycles and productivity shocks can be represented via complex numbers or the Laplace transformation. With the help of this model, new mechanisms of international trade are identified. Four theoretical examples with numerical applications are presented. First, it is demonstrated how an increase in trade from Asia to North America affects the world economy. Second, an intuitive rule for finding the welfare-optimal tariff is derived. Third, three possibilities for vanishing trade effects (fluctuations) are explained: trade diversion, the 'river-island effect', and overlapping business cycles. Fourth, it is shown how adjustment costs delay the propagation of shocks or business cycles.