Effects of degree variability and dependence on cascading failures: A case study of two interdependent systems

We investigate the effects of degree variability and dependence structure on the likelihood of a large-scale failure in a complex system comprising two interdependent systems. The dynamics of failure transmission between agents are modeled using a multi-type branching process. We approximate the likelihood of experiencing an epidemic of failures in a large system, starting with a random failure, using the probability of cascading failures in the branching process. Our findings suggest: (i) higher variability in agents' degrees, which indicate more widely varying levels of interdependence among the agents, makes it less likely to see an outbreak of failures, and (ii) positive correlations in the degrees render the system less susceptible to widespread propagation of failures.