We introduce a novel class of equilibrium metrics (EMs) to quantify spatio-temporal equilibrium of dynamic supply-demand networks defined on the same graph. It is primarily motivated by measuring the local and global spatio-temporal equilibrium between demand and supply networks in large-scale ride-sharing platforms, such as Uber, Lyft, and DiDi. The two key components of EMs are to formulate the spatio-temporal equilibrium problem as an unbalanced optimal transport problem and to develop an efficient linear programming algorithm to solve such transport problem. Specifically, our EMs measure the local (or global) distance between demand and supply patterns after the optimal transport, while incorporating the related transporting cost. We examine the performance of EM in two important applications, including the use of EMs for predicting local and global answer rates and large-scale order dispatch in ride-sharing platform.