Before revision:  Here we study and quantify the impact that the complexity of networks has on contagion effects and system stability, and our focus is on the channel of default contagion that describes the spread of initial distress via direct balance sheet exposures{\em   .
After revision:  Here we study and quantify the impact that the complexity of networks has on contagion effects and system stability, and our focus is on the channel of default contagion that describes the spread of initial distress via direct balance sheet exposures{\em models in which informally the only network parameter is the degree sequence (see (Amini et. al. 2016) and (Detering et. al. 2019) for example) and the contagion process can be described by a one dimensional fix-point equation. These networks fail to account for a pronounced block structure such as core/periphery or a network composed of different connected blocks for different countries .