Networks are all-pervasive in nature. The complete structural controllability of a network and its robustness against unwanted link failures and perturbations are issues of immense concern. In this chapter, we propose a heuristic to determine the minimum number of driver nodes for complete structural control, with a reduced complexity. We also introduce a novel approach to address the vulnerability of the real-world complex networks, and enhance the robustness of the network, prior to an attack or failure. The simulation results reveal that dense and homogenous networks are easier to control with lesser driver nodes, and are more robust, compared to sparse and inhomogeneous networks.
Top1. Introduction
With the recent advances in network sciences and technology, we are compelled to recognize that nothing happens in isolation. Most of the phenomena occurring around us are connected with an enormous number of other pieces of a complex universal puzzle (Tanner, 2004; Barabasi, 2002; Strogatz, 2001). Our biological existence, religious practices and the social world, vividly depict a pellucid story of interrelatedness. With the Internet dominating our lives in the 21st century, we are witnessing a revolution in the making. But, the underlying critical question is: are we ready to embrace the importance of networks around us?
We should learn to appreciate the importance of networks, as part of our daily lives. Recent developments indicate that networks will dominate the next hundreds of years, to a much greater extent than most people are even prepared to acknowledge (Barabasi, 2002; Strogatz, 2001) this fact.
Complex networks are those real-world networks that are characterized by irregular non-trivial topological features, dynamically evolving with time (Strogatz, 2001; Dorogovtsev et al., 2003; Newman et al., 2006; Albert et al., 2002). Different neural networks in our body, various biological networks, the Internet, power-grid (Broder et al., 2000), World Wide Web, social networks etc., can effectively be modeled as complex networks (Strogatz, 2001; Dorogovtsev et al., 2003; Newman et al., 2006). Hence, complex networks form a crucial part of our daily lives (Dorogovtsev et al., 2003). Since the last decade, we have been witnessing a major surge of growing interest and research, with the main focus shifting from the analysis of small networks to that of systems with thousands or millions of nodes. Reductionism was the key driving force behind much of the research of the previous century (Barabasi, 2002). For decades, scientists and researchers have studied atoms and their constituents to understand the universe, molecules to comprehend life, individual gene to characterize and to examine human behavior. Now, relying on the results gathered from the research done in the previous century, we are close to knowing everything about the individual piece. We have successfully disassembled the nature by spending billions of research dollars. But now we are clueless as we run into the hard wall of complexity (Barabasi, 2002; Albert et al., 2002). Nature is not a well-designed puzzle with a unique solution. In complex systems, the components can reassemble in more ways than we can ever imagine. Nature exploits all-encompassing laws of self-organization, whose roots are still mysteries to us (Barabasi, 2002; Newman et al., 2006).