This paper explores the relationship between the structure of financial networks and the likelihood of systemic failures due to counterparty risk. The authors introduce a framework to study how the interbank connectivity affects financial contagion, highlighting a "phase transition" in the system's stability as the degree of interconnectivity increases. They find that under small negative shocks, a more equal distribution of interbank obligations enhances system stability, while dense interconnections can lead to more fragility. However, for large shocks, dense networks become more fragile, and weakly connected networks are less vulnerable. The paper also introduces the concept of harmonic distance, which measures the susceptibility of banks to distress, and shows that banks with lower harmonic distances to a distressed bank are more likely to default. These findings confirm the "robust-yet-fragile" nature of financial networks, where features that enhance resilience under certain conditions can also contribute to systemic risk under others.This paper explores the relationship between the structure of financial networks and the likelihood of systemic failures due to counterparty risk. The authors introduce a framework to study how the interbank connectivity affects financial contagion, highlighting a "phase transition" in the system's stability as the degree of interconnectivity increases. They find that under small negative shocks, a more equal distribution of interbank obligations enhances system stability, while dense interconnections can lead to more fragility. However, for large shocks, dense networks become more fragile, and weakly connected networks are less vulnerable. The paper also introduces the concept of harmonic distance, which measures the susceptibility of banks to distress, and shows that banks with lower harmonic distances to a distressed bank are more likely to default. These findings confirm the "robust-yet-fragile" nature of financial networks, where features that enhance resilience under certain conditions can also contribute to systemic risk under others.