A financial market can be expressed as a network structure in which the stocks reside as nodes and the links account for returns correlation. The centrality measure in the financial network structure captures firms' embeddedness and connectivity in the capital market structure. This paper investigates firms' centrality in the financial network as an explanatory variable in corporate-failure prediction as well as a measure of firms' systemic importance. First, when analyzing credit default swap (CDS) spreads, we find that peripheral firms in the network have higher average CDS spreads and a higher propensity for CDS jump events. Second, centrality is found to increase the explanatory power of default prediction models, and, moreover, it is negatively related to failure and bankruptcy probability. This implies that peripheral firms in the network are more likely to fail. Finally, by examining the out-of-sample performance of centrality as a measure of systemic importance, we find that centrality correctly distinguishes the firms that suffered higher losses during the 2007-8 crisis period.