Research On The Robustness And Controllability Of Complex Networks

Network science is a highly interdisciplinary field ranging from natural science to en-gineering technology and it has been applied to model complex systems and used to explain their behaviors. As the fast development of science and technology, networked systems become interdependent with each other. The interdependence between systems makes the system more complex and show some functions that do not exist in a single network, and at the same time, decrease the robustness of interacting systems and cause a cascade of failures with sometimes catastrophic consequences. How does the interdependence between net-works decrease the system's robustness? what is the mechanism underlying the catastrophic failure? Are these complex network system controllable? These are all crucial questions in complex networks. Answers to these questions could help us understand the real complex systems, find strategies to improve the system robustness, enable to design robust infras-tructure systems and provide instructions on controlling complex networks. Based on the questions above, this dissertation contains the following main contents:A model of interdependent directed networks was built, and a novel theoretical frame-work based on generating functions and percolation theory for understanding the break-down and robustness of interdependent directed networks was developed. We find that for interdependent Erdos-Renyi networks the directionality within each network increases their vulnerability and exhibits new hybrid phase transitions. We also find that the percolation be-havior of interdependent directed scale-free networks with, and without degree correlations is so complex that two criteria are needed to quantify and compare their robustness:the percolation threshold and the integrated size of the giant component during an entire attack process. Interestingly, we find that the in-degree and out-degree correlations in each net-work layer increase the robustness of interdependent degree heterogeneous networks that most real networks are, but decrease the robustness of interdependent networks with ho-mogeneous degree distribution and with strong coupling strengths. Moreover, by applying our theoretical analysis to real interdependent international trade networks, we find that the robustness of these real-world systems increases with the in-degree and out-degree correla-tions, confirming our theoretical analysis.We propose a method for randomly selecting the minimum driver node set, and divide the driver nodes into different categories providing a systematic analysis of the roles of dif-ferent driver nodes in biological systems. In the human liver metabolic network (HLMN), the driver metabolites tend to have strong ability to influence the states of other metabolites and weak susceptibility to be influenced by the states of others. Among the identified 36 crit-ical driver metabolites,27 metabolites were found to be essential; the high-frequency driver metabolites tend to participate in different metabolic pathways, which are important in regu-lating the whole metabolic systems. There are interesting connections between the structural controllability theory and the human liver metabolism:driver metabolites have essential bi-ological functions, which may be potential drug-targets; the crucial role of extracellular metabolites and transport reactions in controlling the HLMN highlights the importance of the environment in the health of human liver metabolism. We find that the proteins in the upstream of the signaling information flow and the low in-degree proteins play a crucial role in controlling the human signaling network. Interestingly, inputting different control signals on the regulators of the cancer-associated genes could cost less than controlling the cancer-associated genes directly in order to control the whole human signaling network in the sense that fewer drive nodes are needed. This research provides a fresh perspective for controlling the human cell signaling system.A method to achieve the goal of choosing partial networks that are easy for controlling and important in networked systems was proposed. By computing the minimum driver nodes densities of the partial networks of ER networks, SF networks and 23 real networks, we find that our method performs better than random method that chooses nodes randomly. Moreover, we find that the nodes chosen by our method tend to be the essential elements of the whole systems, via studying the nodes chosen by our method of a real human signaling network and a human protein interaction network and discovering that the chosen nodes from these networks tend to be cancer-associated genes.An analytic framework to study the controllability of the four types of giant connected component of a directed network with an arbitrary degree distribution was developed.We find that for both ER networks and SF networks with p fraction of remaining nodes, the minimum driver node density to control the giant component first increases and then decreases as p increases from zero to one, showing a peak at a critical point p = pm. Interestingly, for ER networks, the peak value of the driver node density remains the same regardless of its average degree (k), and is determined by pm(k). Moreover, the minimum driver node densities needed to control the giant components of the degree heterogeneous networks are higher than those of the degree homogeneous networks, indicating that the giant components of degree heterogeneous networks are more difficult to control than those of degree homogeneous networks.