This paper analyzes the relationship between the financial network architecture and the likelihood of systemic failures due to counterparty risk contagion. It shows that as interbank interconnectivity increases, financial systems can become more stable under small shocks but more fragile under large shocks. The paper highlights the "robust-yet-fragile" nature of financial networks: features that enhance resilience under certain conditions can also amplify systemic risk under others. The study considers a financial system with n banks, each holding capital and investing in projects that yield returns over two periods. Banks borrow from each other and have obligations to pay senior creditors. The paper introduces a payment equilibrium concept, showing that a mutually consistent set of repayments and liquidations always exists and is generically unique. The paper then examines how the structure of the financial network affects the extent of contagion. It finds that when the magnitude of negative shocks is below a critical threshold, a more equal distribution of interbank liabilities leads to a less fragile system. The complete network, where each bank's liabilities are equally held by all others, is the least prone to contagious defaults, while the ring network, where each bank's liabilities are held by a single counterparty, is the most fragile. However, when the magnitude or number of negative shocks cross certain thresholds, the most fragile networks change. In the presence of large shocks, denser interbank liabilities facilitate contagion and create a more fragile system. In contrast, "weakly connected" networks, where banks have minimal claims on each other, are significantly less fragile. The paper also introduces a new notion of distance over the financial network, the harmonic distance, which captures the susceptibility of each bank to distress at others. It shows that banks with harmonic distances below a certain threshold default when a shock occurs. This highlights that traditional measures of network centrality, such as eigenvector or Bonacich centralities, may not be suitable for identifying systemically important institutions. Instead, the harmonic distance measure is more appropriate in capturing systemic importance. The paper also discusses the role of the network's bottleneck parameter, which measures the minimal extent of interconnectivity between two subsets of banks. It shows that a higher bottleneck parameter corresponds to a more interconnected network, which can be more fragile in the presence of large shocks. Overall, the paper confirms the conjecture that highly interconnected financial networks can be "robust-yet-fragile," where connections serve as shock absorbers within a certain range but can propagate shocks beyond that range, leading to systemic risk. The results highlight the importance of network structure in determining the stability and resilience of financial systems.This paper analyzes the relationship between the financial network architecture and the likelihood of systemic failures due to counterparty risk contagion. It shows that as interbank interconnectivity increases, financial systems can become more stable under small shocks but more fragile under large shocks. The paper highlights the "robust-yet-fragile" nature of financial networks: features that enhance resilience under certain conditions can also amplify systemic risk under others. The study considers a financial system with n banks, each holding capital and investing in projects that yield returns over two periods. Banks borrow from each other and have obligations to pay senior creditors. The paper introduces a payment equilibrium concept, showing that a mutually consistent set of repayments and liquidations always exists and is generically unique. The paper then examines how the structure of the financial network affects the extent of contagion. It finds that when the magnitude of negative shocks is below a critical threshold, a more equal distribution of interbank liabilities leads to a less fragile system. The complete network, where each bank's liabilities are equally held by all others, is the least prone to contagious defaults, while the ring network, where each bank's liabilities are held by a single counterparty, is the most fragile. However, when the magnitude or number of negative shocks cross certain thresholds, the most fragile networks change. In the presence of large shocks, denser interbank liabilities facilitate contagion and create a more fragile system. In contrast, "weakly connected" networks, where banks have minimal claims on each other, are significantly less fragile. The paper also introduces a new notion of distance over the financial network, the harmonic distance, which captures the susceptibility of each bank to distress at others. It shows that banks with harmonic distances below a certain threshold default when a shock occurs. This highlights that traditional measures of network centrality, such as eigenvector or Bonacich centralities, may not be suitable for identifying systemically important institutions. Instead, the harmonic distance measure is more appropriate in capturing systemic importance. The paper also discusses the role of the network's bottleneck parameter, which measures the minimal extent of interconnectivity between two subsets of banks. It shows that a higher bottleneck parameter corresponds to a more interconnected network, which can be more fragile in the presence of large shocks. Overall, the paper confirms the conjecture that highly interconnected financial networks can be "robust-yet-fragile," where connections serve as shock absorbers within a certain range but can propagate shocks beyond that range, leading to systemic risk. The results highlight the importance of network structure in determining the stability and resilience of financial systems.