We model the robustness against random failure or an intentional attack of networks with an arbitrary large-scale structure. We construct a block-based model which incorporates—in a general fashion—both connectivity and interdependence links, as well as arbitrary degree distributions and block correlations. By optimizing the percolation properties of this general class of networks, we identify a simple core-periphery structure as the topology most robust against random failure. In such networks, a distinct and small “core” of nodes with higher degree is responsible for most of the connectivity, functioning as a central “backbone” of the system. This centralized topology remains the optimal structure when other constraints are imposed, such as a given fraction of interdependence links and fixed degree distributions. This distinguishes simple centralized topologies as the most likely to emerge, when robustness against failure is the dominant evolutionary force.
Peixoto, T. P., & Bornholdt, S. (2012). Evolution of robust network topologies: emergence of central backbones. Physical Review Letters, 109(11), . https://doi.org/10.1103/PhysRevLett.109.118703