Throughout the past decade, there has been a significant advance in understanding the structure and function of networks, and mathematical models of networks are now widely used to describe a broad range of complex systems, such as socio-economic systems. However, the significant majority of methods have dealt almost exclusively with individual networks treated as isolated systems. In reality an individual network is often just one component in a much larger complex multi-level network (network of networks, NON). The NON framework provides critical new insights into the structure and function of real-world complex systems. One such insight is that NON system is significantly more vulnerable to shocks and damages, which has lead to the development of the theory of cascading failures in interdependent networks. Here we provide an overview of this theory, and one example of its application to economic systems.
IntroductionThe growth of technology, globalization, and urbanization has caused world-wide human social and economic activities to become increasingly interdependent [1][2][3][4][5][6][7][8][9][10][11][12][13]. From the recent financial crisis it is clear that components of this complex system have become increasingly susceptible to collapse. Current models have been unable to predict instability, provide scenarios for future stability, or control or even mitigate systemic failure. Thus, there is a need of new ways of quantifying complex system vulnerabilities as well as new strategies for mitigating systemic damage and increasing system resiliency [14,15]. Achieving this would also provide new insight into such key issues as financial contagion [16,17] and systemic risk [18][19][20] and would provide a way of maintaining economic and financial stability in the future.