  We investigate robustness of correlated networks against propagating attacks
modeled by a susceptible-infected-removed model. By Monte-Carlo simulations, we
numerically determine the first critical infection rate, above which a global
outbreak of disease occurs, and the second critical infection rate, above which
disease disintegrates the network. Our result shows that correlated networks
are robust compared to the uncorrelated ones, regardless of whether they are
assortative or disassortative, when a fraction of infected nodes in an initial
state is not too large. For large initial fraction, disassortative network
becomes fragile while assortative network holds robustness. This behavior is
related to the layered network structure inevitably generated by a rewiring
procedure we adopt to realize correlated networks.
