For systemic risk, the impact of the financial network's characteristics remains imperfectly understood at best, even if the view that network structure is closely related to systemic risk has become a broad consensus. By choosing S&P 500 constituents as the research sample, we investigate the structural characteristics of the Engle-Granger networks and explore the impact of network centrality on one-quarter-ahead systemic risk. We find that a firm's network centrality is positively related to both dimensions of its systemic risk (i.e. the firm's vulnerability to, and contribution to, system-wide downturns). The results remain robust after we consider the potential endogeneity and various sensitivity checks. An examination of potential channels reveals that centrally located firms in the network have a high extent of co-movement with the market, and are likely to trigger systemic market failures caused by stock price crashes in clusters once they fall into a downturn. We further show that the positive relation between network centrality and future systemic risk is more salient for financial firms and more pronounced during recessions.