Resilience of Networks Formed of Interdependent Modular Networks

TL;DR

This paper develops a theoretical framework to analyze the resilience of interdependent modular networks, revealing how modularity influences failure transitions and resilience in infrastructure systems.

Contribution

It introduces a novel theoretical model for interdependent modular networks and characterizes different failure regimes based on the number of modules and their interconnections.

Findings

Fewer modules with strong intraconnections cause an abrupt first-order transition and subsequent percolation.

More modules with many interconnections lead to a single transition.

Modular structure significantly affects the failure dynamics and resilience of interdependent networks.

Abstract

Many infrastructure networks have a modular structure and are also interdependent. While significant research has explored the resilience of interdependent networks, there has been no analysis of the effects of modularity. Here we develop a theoretical framework for attacks on interdependent modular networks and support our results by simulations. We focus on the case where each network has the same number of communities and the dependency links are restricted to be between pairs of communities of different networks. This is very realistic for infrastructure across cities. Each city has its own infrastructures and different infrastructures are dependent within the city. However, each infrastructure is connected within and between cities. For example, a power grid will connect many cities as will a communication network, yet a power station and communication tower that are interdependent will likely be in the same city. It has been shown that single networks are very susceptible to the failure of the interconnected nodes (between communities) Shai et al. and that attacks on these nodes are more crippling than attacks based on betweenness da Cunha et al. In our example of cities these nodes have long range links which are more likely to fail. For both treelike and looplike interdependent modular networks we find distinct regimes depending on the number of modules, $m$. (i) In the case where there are fewer modules with strong intraconnections, the system first separates into modules in an abrupt first-order transition and then each module undergoes a second percolation transition. (ii) When there are more modules with many interconnections between them, the system undergoes a single transition. Overall, we find that modular structure can influence the type of transitions observed in interdependent networks and should be considered in attempts to make interdependent networks more resilient.