The effect of capacity redundancy disparity on the robustness of interconnected networks

• We consider the model where two networks with different capacity redundancy are interconnected.
• We show that it is possible that more capacity redundancy may cause worse robustness.
• We compare different cases and find that this counterintuitive feature only appears in interconnected networks with redundancy disparity.

Cascading failures in interconnected networks have received more and more attention. In previous works, the basic assumption is that networks share the same capacity redundancy. However, this setting cannot capture the real case very well. Hence, in this paper, we analyze the effect of capacity redundancy disparity on the robustness of interconnected networks. In isolated networks, it is well known that the complex network’s robustness can be improved by increasing its capacity redundancy. In interconnected networks where two networks share the same capacity redundancy, the similar result holds. Yet this result is not necessarily true in interconnected networks where two networks are different in capacity redundancy. We find that when the capacity redundancy of one network is fixed, the robustness of the whole system may not follow another network’s capacity redundancy. More specifically, when the fixed network’s capacity redundancy is very small or very large, the robustness of the whole system increases as another network’s capacity redundancy increases. But there exists a certain range within which the increase of one network’s capacity redundancy results in the robustness decline of the whole system. This counterintuitive feature appears under different coupling patterns such as assortative, disassortative, or random coupling. This result advances our understanding of the robustness of interconnected networks.