Characteristics of robust complex networks - Sydney, Ali (Kansas State University, 2009)
In network theory, a complex network represents a system whose evolving structure and dynamic behavior contribute to its robustness. The study of complex networks, though young, spans diverse domains including engineering, science, biology, sociology, psychology, and business, to name a few. Regardless of the ﬁeld of interest, robustness defines a network’s survivability in the advent of classical component failures and at the onset of cryptic malicious attacks. With increasingly ambitious initiatives such as GENI and FIND that seek to design future internets, it becomes imperative to define the characteristics of robust topologies, and to build future networks optimized for robustness. This thesis investigates the characteristics of network topologies that maintain a high level of throughput in spite of multiple attacks. To this end, we select network topologies belonging to the main network models and some real world networks. We consider three types of attacks: removal of random nodes, high degree nodes, and high betweenness nodes. We use elasticity as our robustness measure and, through our analysis, illustrate that different topologies can have different degrees of robustness. In particular, elasticity can fall as low as 0.8% of the upper bound based on the attack employed. This result substantiates the need for optimized network topology design. Furthermore, we implement a trade off function that combines elasticity under the three attack strategies and considers the cost of the network. Our extensive simulations show that, for a given network density, regular and semi-regular topologies can have higher degrees of robustness than heterogeneous topologies, and that link redundancy is a sufficient but not necessary condition for robustness.
Keywords: Complex Networks; Robustness; Optimization; Attack; Trade off; Topology; Engineering, Electronics and Electrical (0544); Engineering, General (0537); Mathematics (0405)