Motivated by the deregulation of electricity market, we study the efficiency loss of the supply function equilibrium (SFE). Specifically, we consider a market where the demand is inelastic, the suppliers submit their supply functions, and a uniform price is set to clear the market. Existing literature has answers to this question without regard to the network structure of the market. However, in many markets (such as electricity markets), there is an underlying physical network that limits the market operations (e.g., in electricity markets, the transmission network determines how electricity flows through the network and thus puts constraints on the supply profile). Motivated by electricity markets, we study how network topology affects the efficiency of SFE. For general mesh networks, we show that the efficiency loss is upper bounded as in the case without networks. Interestingly, we find a class of radial networks, for which the efficiency loss is independent of the local network topology.