Robustness of Multilayer Networks: A Graph Energy Perspective

作     者：Kumar, Rajesh Kumari, Suchi Mishra, Anubhav 

作者机构：College of Engineering and Design Alliance University Bangalore India School of Computer Science Engineering and Technology Bennett University Greater Noida India Ghani Khan Choudhary Institute of Engineering and Technology West Bengal Malda India 

出 版 物：《SSRN》 

年 卷 期：2023年

核心收录：

主　　题：Laplace transforms 

摘      要：Real-world complex systems such as Social, Technological, Infrastructure, etc., are inter-connected and interdependent. These systems are vulnerable to attacks failing nodes/edges. Most of the recent research works involve the study of robustness by evaluating the size of the largest connected component. For a given network size, the value of the size of the largest connected component is $1$ for the complete network. However, in the event of the cascade failure (attack) of some fraction of edges, the network becomes sparse and still may be the size of the largest connected component is $1$. There may be an instance at which the network system is critical, and any small perturbation may disintegrate the network system. Thus, in the present work, the robustness of the multilayer network system is evaluated by computing the efficiency and Laplacian and Quantum energies of the system during the cascade failure. Simulation results reveal that during the cascade failure, efficiency and Laplacian energy keep on decreasing up to some initial instances, and the robustness index is $1$. However, there is a critical point at which the system starts disintegrating for the given values of efficiency and Laplacian energy. For the Quantum energy scenario, the system is stable with minimum energy. During the cascade failure, the system begins to become unstable showing the increase in the Quantum energy at some critical point, and the robustness index begins to decrease. © 2023, The Authors. All rights reserved.