In this thesis, we develop a novel stochastic modeling approach based on multiple interdependent topological measures of complex networks. The key engine behind our approach is to evaluate the dynamics of multiple network motifs as descriptors of the underlying network topology. Under a framework of the gamma degradation model, we develop a formal statistical framework for the analysis of reliability and robustness of a single complex network as well as for assessing differences in reliability properties exhibited by two different networks. We validate the proposed methodology with Monte Carlo simulation studies and illustrate the utility of the proposed approach by performing a vulnerability analysis of European power grid networks under various targeted attacks.
Furthermore, we also consider cyber systems and computer infrastructures for commerce and communications such as cyberspace, the Internet, electronic payment systems. To understand the risks of complex networks, we propose a modified Wiener process model for the degeneration of the network functionality upon the removal of nodes due to attacks or malfunctions. We also propose three statistical testing procedures based on the Wiener process model to compare the resilience of two different networks, which can be used to comparing risks in the cybersecurity insurance domain. The proposed methodologies can be applied to any topological measures of network robustness or risk. A practical data analysis for a peer-to-peer file-sharing network is presented to illustrate the proposed model and methods. Monte Carlo simulations are used to evaluate the performance of the proposed methodologies and practical recommendations are provided.
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Chen, Yuzhou, "Modified Degradation Process Models and Statistical Methods for Assessing Robustness and Reliability of Complex Networks" (2021). Statistical Science Theses and Dissertations. 23.