On The Repair Strategy And Correlation Properties Of Complex Networks Under Attacks

This dissertation is concerned with the study of the repair strategy and correlation properties of complex networks under attacks; with the study of topological properties of US airport network and the resilience under errors and attacks."errors" and " attacks" are two simulation strategies to investigate the dynamics of complex networks. Error is simulated as the deletion of network nodes or links chosen at random, while intentional attack as targeted removal of a specific class of nodes or links, such as nodes with highest degrees.We propose a repair strategy of complex networks under the attacks. With the repair strategy, we study the stability and correlation properties of Erdo|¨s-Rényi random graphs, Watts-Strogatz small-world networks and Barabási-Albert scale-free networks, especially the corresponding topological changes of these three complex networks.A new quality, invulnerabilty I(s), is introduced. I(s) reflects the tolerance of complex networks under attacks. I(s) is a step-wise non-decreasing function and reaches a constant value I_c, the stationary state, after millions of steps of evolution. I_c is the maximum value in the stationary state, which exhibits that the system is getting safer and more invulnerable under continuous attacks and repairs. On the other hand, the maximum degree in the stationary state, (k_max)_c, is the minimum in the system.For the study of Erdo|¨s-Rényi random networks in the stationary state, I_c is independent of network size N and connection probability p, but has a power-law dependence on the average degree = pN. I_c also has a power-law relationship with the repair probability p_re, with the exponent τ decreasing with the increasing of network size N.Barabási-Albert scale-free networks with power law degree distribution, is a completely different topological structure from random graphs with exponential degree distribution. For the scale-free networks in the stationary state, I_c is slightly greater than that of the random graph under the same network size N and repair probability p_re. Correspondingly, the maximum degree in the stationary state (k_max)_c is slightly less...