This paper introduces a novel form of moral hazard specific to networks and illustrates this concept using simple models from coordination games, epidemics, supply chains, and financial networks. In these models, agents form beneficial links that also propagate costly contagion. Endogenously, second-order contagion risk constrains the concentration of connections around central agents. Protective measures against contagion, such as vaccines, subsidies, or bailouts, mitigate contagion risk, subsequently increasing concentration. However, if these protective measures are imperfect or costly, shocks to central agents can result in greater harm and increased welfare variance, as evidenced in disease outbreaks, aggregate volatility, or financial crises.