Does Isolating High-Modularity Communities Prevent Cascading Failure?

Communities are often defined as sets of nodes that are more densely connected to each other than to those outside the community, i.e., high-modularity partitions. It seems obvious that isolating high-modularity communities is a good way to prevent the spread of cascading failures. Here we develop a heuristic approach informed by Moore-Shannon network reliability that focuses on dynamics rather than topology. It defines communities directly in terms of the size of cascades they allow. We demonstrate that isolating communities defined this way may control cascading failure better. Moreover, this approach is sensitive to the values of dynamical parameters and allows for problem-specific constraints such as cost.