Introduction to networks of networks. (2022)

• Record Type: Book
• Further Information: Note: Jainxi Gao, Amir Bashan, Louis Shekhtman, Shlomo Havlin.
• Authors: Gao, Jainxi; Bashan, Amir; Shekhtman, Louis; Havlin, Shlomo
• Contents: Preface 1 Basic concepts of single networks. . . . . . . . . . . . . . . 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1; 1.2 Degree distribution—How networks are structured? . . . . . . . . . . .2; 1.2.1 Types of networks . . . . . . . . . . . . . . . . . . . . . . . . .2; 1.2.2 Degree and degree distributions . . . . . . . . . . . . . . . . . .3; 1.2.3 Generating functions . . . . . . . . . . . . . . . . . . . . . . . .5; 1.3 Percolation transition—How a network collapses? . . . . . . . . . . . .6; 1.3.1 Failure and attack . . . . . . . . . . . . . . . . . . . . . . . . .7; 1.3.2 Giant component . . . . . . . . . . . . . . . . . . . . . . . . . .9; 1.3.3 Critical threshold . . . . . . . . . . . . . . . . . . . . . . . . . .12; 1.4 Further network properties . . . . . . . . . . . . . . . . . . . . . . . . . 13; 1.5 Spatial networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2 From single network to network of networks 25; 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25; 2.2 How networks network? . . . . . . . . . . . . . . . . . . . . . . . . . . 26; 2.2.1 When a single network is not enough: examples of interactingnetworks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26; 2.2.2 Zoology of network of networks . . . . . . . . . . . . . . . . . . 27; 2.3 Key phenomena in network of networks . . . . . . . . . . . . . . . . . . 29; 2.3.1 Cascading failures in interdependent networks . . . . . . . . . . 29; 2.3.2 Increased resilience of interconnected networks . . . . . . . . . . 31; 2.3.3 Dynamics on network of networks . . . . . . . . . . . . . . . . . 32 3 A pair of interdependent networks 41; 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41; 3.2 Different types of coupling . . . . . . . . . . . . . . . . . . . . . . . . . 42; 3.2.1 Feedback condition . . . . . . . . . . . . . . . . . . . . . . . . . 42; 3.2.2 No-Feedback condition . . . . . . . . . . . . . . . . . . . . . . . 43; 3.2.3 Multiple support . . . . . . . . . . . . . . . . . . . . . . . . . . 44; 3.3 Structural percolation . . . . . . . . . . . . . . . . . . . . . . . . . . . 45; 3.3.1 Fully interdependent networks . . . . . . . . . . . . . . . . . . . 45; 3.3.2 Partially interdependent networks . . . . . . . . . . . . . . . . . 49; 3.3.3 Networks with multiple support . . . . . . . . . . . . . . . . . . 53; 3.3.4 Interconnected networks . . . . . . . . . . . . . . . . . . . . . . 58; 3.3.5 Antagonistic networks . . . . . . . . . . . . . . . . . . . . . . . 62; 3.4 Targeted attack on partially interdependent networks . . . . . . . . . . 66 4 Robustness of networks of interdependent networks 77; 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77; 4.2 Structures of networks of networks (NON) . . . . . . . . . . . . . . . . 79; 4.2.1 Loopless network of networks . . . . . . . . . . . . . . . . . . . 79; 4.2.2 Loop-like network of networks . . . . . . . . . . . . . . . . . . . 79; 4.2.3 Regular network of random networks . . . . . . . . . . . . . . . 79; 4.2.4 Replica nodes in network of networks . . . . . . . . . . . . . . . 79; 4.3 Cascading Failures in a Network of Networks . . . . . . . . . . . . . . . 79; 4.3.1 Dynamic process . . . . . . . . . . . . . . . . . . . . . . . . . . 80; 4.3.2 Identical steady state results for all tree-like structures . . . . . 85; 4.3.3 General Stationary State . . . . . . . . . . . . . . . . . . . . . . 86; 4.4 Percolation of network of networks . . . . . . . . . . . . . . . . . . . . 88; 4.4.1 Percolation of tree-like network of networks . . . . . . . . . . . 88; 4.4.2 Percolation of a RR NON composed of random networks . . . . 93; 4.5 Comparing Feedback and No-Feedback Conditions . . . . . . . . . . . . 99; 4.6 Vulnerability of network of networks for large number of networks . . . 101 5 Spatially embedded interdependent networks 131; 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131; 5.2 The extreme vulnerability of semi-spatial interdependent networks . . . 133; 5.2.1 Percolation transition in semi-spatial interdependent networks . 134; 5.2.2 In semi-spatial interdependent networks qc = 0 . . . . . . . . . . 135; 5.2.3 Critical exponents of the percolation transition . . . . . . . . . 136; 5.3 Semi-spatial model of network of networks . . . . . . . . . . . . . . . . 137; 5.3.1 Tree-like network of interdependent networks . . . . . . . . . . 137; 5.3.2 Star-like network of interdependent networks . . . . . . . . . . 139; 5.3.3 Random regular network formed of interdependent spatiallyembedded networks . . . . . . . . . . . . . . . . . . . . . . . . . 139; 5.4 Fully-spatial interdependent networks: propagation of cascading failures 140; 5.5 Effect of dependency link length, the r-model . . . . . . . . . . . . . . 141; 5.5.1 Theoretical model of spatial failure propagation . . . . . . . . . 142; 5.5.2 Cascades propagation due to random failures . . . . . . . . . . 143; 5.6 Effect of connectivity link length, the ζ-model . . . . . . . . . . . . . . 144; 5.7 Localized attacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145; 5.7.1 Localized attacks on spatial networks with short-range dependency links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145; 5.7.2 Localized attacks on spatial multiplexes . . . . . . . . . . . . . 149; 5.7.3 Spatial multiplexes with community structure . . . . . . . . . . 150 6 Further Features in Networks of Networks 174; 6.1 Synchronization and Dynamics on Networks of Networks . . . . . . . . 174; 6.2 Different network structures in networks of networks . . . . . . . . . . 176; 6.2.1 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176; 6.2.2 Node correlations . . . . . . . . . . . . . . . . . . . . . . . . . . 177; 6.2.3 Directed networks . . . . . . . . . . . . . . . . . . . . . . . . . 177; 6.2.4 Community Structure . . . . . . . . . . . . . . . . . . . . . . . 177; 6.3 Overlap and Intersimilarity in Networks of Networks . . . . . . . . . . 178; 6.4 Different percolation processes in networks of networks . . . . . . . . . 178; 6.4.1 Bond Percolation . . . . . . . . . . . . . . . . . . . . . . . . . . 178; 6.4.2 Reinforced nodes . . . . . . . . . . . . . . . . . . . . . . . . . . 179; 6.4.3 Combining k-core and interdependent percolation . . . . . . . . 179; 6.5 Multimodal transportation . . . . . . . . . . . . . . . . . . . . . . . . . 179; 6.6 Games on networks of networks . . . . . . . . . . . . . . . . . . . . . . 180; 6.7 Controllability in a network of networks . . . . . . . . . . . . . . . . . 180
• Publisher Details: Bristol : IOP Publishing
• Publication Date: 2022
• Extent: 1 online resource, illustrations (black and white, and colour)
• Subjects: 003; System analysis
• Languages: English
• ISBNs: 9780750310468; 9780750311168
• Related ISBNs: 9780750310475
• Notes: Note: Description based on CIP data; resource not viewed.
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