  Propagation of balance-sheet or cash-flow insolvency across financial
institutions may be modeled as a cascade process on a network representing
their mutual exposures. We derive rigorous asymptotic results for the magnitude
of contagion in a large financial network and give an analytical expression for
the asymptotic fraction of defaults, in terms of network characteristics. Our
results extend previous studies on contagion in random graphs to inhomogeneous
directed graphs with a given degree sequence and arbitrary distribution of
weights. We introduce a criterion for the resilience of a large financial
network to the insolvency of a small group of financial institutions and
quantify how contagion amplifies small shocks to the network. Our results
emphasize the role played by "contagious links" and show that institutions
which contribute most to network instability in case of default have both large
connectivity and a large fraction of contagious links. The asymptotic results
show good agreement with simulations for networks with realistic sizes.
