Measuring cascade effects in coupled networks using algebraic connectivity

Understanding how the underlying network structure and interconnectivity impact on robustness of the coupled networks is a major challenge in complex networks studies. There are some existing metrics that can be used to measure network robustness. However, different metrics such as the average node degree, interpret different characteristic of network topological structure, especially less metrics have been identified to effectively measure the cascade performance in coupled networks. In this paper, we propose to use a combined Laplacian matrix to model the coupled networks and their interconnectivity, and then use its algebraic connectivity metric as a measure to its cascading behavior. Moreover, we have conducted extensive comparative studies among different metrics such as the average node degree, and the proposed algebraic connectivity. We have found that the algebraic connectivity metric can describe more accurate and finer characteristics on topological structure of coupled networks than other metrics widely adapted by the existing research studies for measuring the cascading performance in coupled networks.