We extend analytic large network results on default contagion in random graphs to capture a pronounced Block Model structure. This includes as a special case the Core-Periphery network structure, which plays a prominent role in recent research on systemic risk. Further, in the existing literature on systemic risk using random graph methods the problematic assumption that the distribution of liabilities solely depends on the creditor type seems to persist. Under this assumption a straightforward application of the law of large numbers allows to turn edge related random elements into deterministic vertex properties. Here we study a general setting in which the liabilities may depend on both the creditor and the debtor where this argument breaks down and a direct asymptotic analysis of the edge weighted random graph becomes necessary. Among several other applications our results allow us to obtain resilience conditions for the entire network (for example the global financial network) based only on subnetwork conditions. Contrasting earlier research we also give an example that demonstrates how reshuffling edge weights to form blocks can in fact impact resilience even for otherwise very homogeneous networks.
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