Introduction to Network of Networks

Description

The interdisciplinary field of network science has attracted enormous attention in recent years, although most results in the field have been obtained by analysing isolated networks. However, many real-world networks do interact with and depend on other networks. In such a network of interacting networks, the system displays surprising and rich behaviour where the failure of nodes in one network may lead to the failure of dependent nodes in other networks. This may happen recursively and can lead to a cascade of failures. In fact, a failure of a very small fraction of nodes in one network may lead to the complete fragmentation of a system of several interdependent networks. Such networks of networks are common and diverse critical infrastructures are frequently coupled together, including systems such as water, food and fuel supply, communications, financial markets and power supply. Different systems in our body, the brain, the respiratory and cardiac systems etc, regularly interact and are interdependent on each other. Moreover, social networks, such as Facebook and Twitter, which play an important role in our life, connect us to a huge system of interacting networks. Thus, understanding network of networks is important for many disciplines and has real-world applications. This book will be the first to discuss this new developing and exciting topic – robustness of network of networks – which can be regarded as a second revolution in network science and will be essential reading for a wide range of physicists, mathematicians, computer scientists, biologists, engineers and social scientists. It is expected to help both students and researchers in the network science field to discover the new fascinating phenomenon in the emerging field of network of networks. PRELIMS.pdf Preface Acknowledgements Author biographies Jianxi Gao Amir Bashan Louis Shekhtman Shlomo Havlin CH001.pdf Chapter 1 Basic concepts of single networks 1.1 Introduction 1.2 Degree distribution—how networks are structured? 1.2.1 Types of networks 1.2.2 Degree and degree distributions 1.2.3 Generating functions 1.3 Percolation transition—how a network collapses? 1.3.1 Failure and attack 1.3.2 Calculating the size of the giant component 1.3.3 Calculating the critical threshold 1.4 Further network properties 1.5 Spatial networks References CH002.pdf Chapter 2 From single networks to networks of networks 2.1 Introduction 2.2 How networks network? 2.2.1 When a single network is not enough: examples of interacting networks 2.2.2 Zoology of network of networks 2.3 Key phenomena in network of networks 2.3.1 Cascading failures in interdependent networks 2.3.2 Increased robustness of interconnected networks 2.3.3 Dynamics on network of networks References CH003.pdf Chapter 3 A pair of interdependent networks 3.1 Introduction 3.2 Different types of dependency between networks 3.2.1 Feedback condition 3.2.2 No-feedback condition 3.2.3 Multiple support 3.3 Random failures 3.3.1 Fully interdependent networks 3.3.2 Partially interdependent networks 3.3.3 Networks with multiple support 3.3.4 Interconnected networks 3.3.5 Antagonistic networks 3.4 Targeted attack on partially interdependent networks References CH004.pdf Chapter 4 Robustness of networks composed of interdependent networks 4.1 Introduction 4.2 Structures of networks of networks (NON) Loopless network of networks Loop-like network of networks Random regular network of random networks Replica nodes in network of networks 4.3 Cascading failures in a network of networks 4.3.1 Dynamic process 4.3.2 Identical steady state results for all tree-like structures 4.3.3 General stationary state 4.4 Percolation of network of networks 4.4.1 Percolation of tree-like network of networks 4.4.2 Percolation of an RR NON composed of random networks 4.5 Comparing feedback and no-feedback conditions 4.6 Vulnerability of network of networks for a large number of networks References CH005.pdf Chapter 5 Spatially embedded interdependent networks 5.1 Introduction 5.2 The extreme vulnerability of semi-spatial interdependent networks 5.2.1 Percolation transition in semi-spatial interdependent networks 5.2.2 In semi-spatial interdependent networks qc=0 5.2.3 Critical exponents of the percolation transition 5.3 Semi-spatial model of network of networks 5.3.1 Tree-like network of interdependent networks 5.3.2 Star-like network of interdependent networks 5.3.3 Random regular network formed of interdependent spatially embedded networks 5.4 Fully-spatial interdependent networks: propagation of cascading failures 5.5 Effect of dependency link length, the r-model 5.5.1 Theoretical model of spatial failure propagation 5.5.2 Cascades propagation due to random failures 5.6 Effect of connectivity link length, the ζ-model The spatial multiplex ζ-model 5.7 Localized attacks 5.7.1 Localized attacks on spatial networks with short-range dependency links 5.7.2 Localized attacks on spatial multiplexes 5.7.3 Spatial multiplexes with community structure References CH006.pdf Chapter 6 Further features in networks of networks 6.1 Synchronization and dynamics on networks of networks 6.2 Different network structures in networks of networks 6.2.1 Clustering 6.2.2 Node correlations 6.2.3 Directed networks 6.2.4 Community structure 6.3 Overlap and intersimilarity in networks of networks 6.4 Different percolation processes in networks of networks 6.4.1 Bond percolation 6.4.2 Reinforced nodes 6.4.3 Combining k-core and interdependent percolation 6.5 Multimodal transportation 6.6 Games on networks of networks 6.7 Controllability of a network of networks 6.8 Interdependent superconducting networks References