Directed complex networks and their structure and dynamics under link deletion

Abstract

Complex networks with their ability to model the essential elements of a system of interacting entities have become a versatile tool with immense scope for application Network science as a tool has found relevance in studying physical biological and chemical systems transport systems social systems medicine finance and risk etc While there are many different aspects to a complete and systematic study of complex networks one of the more important properties is their robustness to perturbation In this thesis we are particularly interested in those types of perturbations that result in loss of connectivity of the network We focus our study on the effects of loss of links in directed complex networks Investigating the performance of a network when it is subject to loss of links helps to design precautionary measures introduce fail safes and implement alternate solutions thus resulting in improved overall performance Alternatively it can also be used to design effective strategies to maximally disrupt the connectivity in a network With this very concise motivation we set out to explore the structural and dynamical response of directed networks to failures random loss of links and attacks targeted removal of links The organization of the thesis is as follows In chapter 1 we provide a brief introduction to the field of complex networks discuss their wide range of applications and ever increasing relevance From local to intermediate to global scales we define the most important and relevant network properties and their corresponding measures Based on these properties we discuss some standard models of network generation their advantages and limitations We finish with a brief mention of a couple of dynamical processes taking place on networks In chapter 2 we introduce methods based on degree preserving rewiring DPR to tune clustering and degree correlations in random and scale free directed networks They provide null models to investigate the role of the mentioned properties along with their s newline newline