Conclusion
Based on the MMA concept, we have proposed a model of interdependent MMA networks, where any node with degree k can be an MMA node with probability kγ. Here, if an MMA node disconnects from the giant component, it can use other methods to reestablish a connection. We have theoretically analyzed the percolation process of the proposed model and derived equations for the giant component. Furthermore, we introduced a method to calculate the discontinuous phase transition point for interdependent networks with arbitrary degree distributions. In addition, our simulation results agree well with our theoretical analyses. We found that the discontinuous phase transition point decreases with increasing γ, and, when γ is greater than a certain value, the phase transition type transfers to continuous. In conclusion, interdependent networks become more robust with an increasing number of MMA nodes.
References
Albert R, Barabási A L. Statistical mechanics of complex networks. Rev Mod Phys, 2002, 74: 47–97
Buldyrev S V, Parshani R, Paul G, et al. Catastrophic cascade of failures in interdependent networks. Nature, 2010, 464: 1025–1028
Parshani R, Buldyrev S V, Havlin S. Interdependent networks: reducing the coupling strength leads to a change from a first to second order percolation transition. Phys Rev Lett, 2010, 105: 048701
Zhou D, Stanley H E, D’Agostino G, et al. Assortativity decreases the robustness of interdependent networks. Phys Rev E, 2012, 86: 066103
La Rocca C E, Stanley H E, Braunstein L A. Strategy for stopping failure cascades in interdependent networks. Phys A-Stat Mech its Appl, 2018, 508: 577–583
Yuan X, Hu Y Q, Stanley H E, et al. Eradicating catastrophic collapse in interdependent networks via reinforced nodes. Proc Natl Acad Sci USA, 2017, 114: 3311–3315
Wu J X. Thoughts on the development of novel network technology. Sci China Inf Sci, 2018, 61: 101301
Erdös P, Rényi A. On random graphs. Publ Math, 1959, 6: 290–297
Barabási A L, Albert R. Emergence of scaling in random networks. Science, 1999, 286: 509–512
Acknowledgements
This work was supported by National Key Research and Development Program of China (Grant No. 2018YFB0804002), National Natural Science Foundation of China (Grant No. 61872382), and Research and Development Program in Key Areas of Guangdong Province of China (Grant No. 2018B010113001).
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Han, W., Tian, L., Zhang, F. et al. Robustness of interdependent multi-model addressing networks. Sci. China Inf. Sci. 64, 169304 (2021). https://doi.org/10.1007/s11432-019-2892-0
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DOI: https://doi.org/10.1007/s11432-019-2892-0