Open AccessMultiple phase transitions in ER edge-coupled interdependent networks
Author(s) -
Yanli Gao,
Jun Liu,
haiwei He,
Jie Zhou,
Shiming Chen
Publication year - 2022
Publication title -
new journal of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.584
H-Index - 190
ISSN - 1367-2630
DOI - 10.1088/1367-2630/ac5055
Subject(s) - robustness (evolution) , interdependent networks , interdependence , coupling strength , physics , coupling (piping) , enhanced data rates for gsm evolution , percolation (cognitive psychology) , topology (electrical circuits) , statistical physics , node (physics) , degree distribution , complex network , computer science , artificial intelligence , combinatorics , mathematics , quantum mechanics , condensed matter physics , engineering , mechanical engineering , biochemistry , chemistry , neuroscience , biology , world wide web , gene , political science , law
Considering the real-world scenarios that there are interactions between edges in different networks and each network has different topological structure and size, we introduce a model of interdependent networks with arbitrary edge-coupling strength, in which q A and q B are used to represent the edge-coupling strength of network A and network B respectively. A mathematical framework using generating functions is developed based on self-consistent probabilities approach, which is verified by computer simulations. In particular, we carry out this mathematical framework on the Erdös–Rényi edge-coupled interdependent networks to calculate the values of phase transition thresholds and the critical coupling strengths which distinguish different types of transitions. Moreover, as contrast to the corresponding node-coupled interdependent networks, we find that for edge-coupled interdependent networks the critical coupling strengths are smaller, and the critical thresholds as well, which means the robustness of partially edge-coupled interdependent networks is better than that of partially node-coupled interdependent networks. Furthermore, we find that network A will have hybrid percolation behaviors as long as the coupling strength q A belongs to a certain range, and the range does not affected by average degree of network A . Our findings may fill the gap of understanding the robustness of edge-coupled interdependent networks with arbitrary coupling strength, and have significant meaning for network security design and optimization.