We propose a new measure of systemic risk based on interconnectedness, defined as the level of direct and indirect links between financial institutions in a correlation-based network. Deriving interconnectedness in terms of risk, we empirically show that within a financial network, indirect links are strengthened during systemic events. The relevance of our measure is illustrated at both local and global levels. Our framework offers policymakers a useful toolbox for exploring the real-time topology of the complex structure of dependencies in financial systems and for measuring the consequences of regulatory decisions.