Effect of network size on robustness of interconnected networks under targeted attack

Cascading failures in coupled networks have been intensively studied recently. The underlying assumption is that all networks share the same size. However, this setting cannot capture real-world coupled networks very well. Hence, in this paper, we explore how different network sizes affect cascades from the perspective of the whole interconnected networks. We find that when two networks with similar sizes are coupled, the interconnected networks are the most fragile for sparse coupling while they are the most robust for dense coupling. Moreover, we also study the effect of network size on the robustness of individual network. We find that when two networks with different sizes are coupled, the larger one is more robust for sparse coupling, while more fragile for dense coupling.