Robustness of n interdependent networks with partial support-dependence relationship

¹ Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University - Zhenjiang, 212013, China
² Center for Polymer Studies and Department of Physics, Boston University - Boston, MA 02215, USA
³ College of Mathematics Science, Chongqing Normal University - Chongqing, 401331, China

Received: 21 March 2013
Accepted: 5 June 2013

Abstract

We study both analytically and numerically the robustness of n interdependent networks with partial support-dependence relationship, which reflects real-world networks more realistically. For a starlike network of n Erdős-Rényi (ER) networks, we find that the system undergoes from second-order to first-order phase transition as coupling strength q increases. Moreover, we notice that the region of the first-order transition becomes larger, while the region of the second-order transition becomes smaller as the number of networks n increases. However, for a starlike network of n scale-free (SF) networks, the system undergoes from second-order through hybrid-order to first-order phase transition as q increases. Furthermore, we also observe that the region of the first-order transition remains constant and appears only for q = 1, however, the region of hybrid-order transition gradually becomes larger and the region of the second-order transition becomes smaller as n increases. For a looplike network of n ER networks, we find the giant component p_∞ to be independent of the number of networks. Additionally, when the average degree of networks increases, the region of the first-order transition becomes smaller and the region of the second-order transition becomes larger. For the case of n ER networks with partial support-dependence relationship, as average supported degree , n coupled networks become independent and only second-order transition is observed, which is similar to q = 0.