Reliability theory for diffusion processes on interconnected networks

We present the concept of network reliability as a framework to study diffusion dynamics in interdependent networks. We illustrate how different outcomes of diffusion processes, such as cascading failure, can be studied by estimating the reliability polynomial under different reliability rules. As an example, we investigate the effect of structural properties on diffusion dynamics for a few different topologies of two coupled networks. We evaluate the effect of varying the probability of failure propagating along the edges, both within a single network as well as between the networks. We exhibit the sensitivity of interdependent network reliability and connectivity to edge failures in each topology.